Apparatus and method for sweeping an image beam in one dimension and bidirectionally sweeping an image beam in a second dimension

Priority claim

The present application claims priority under US Provisional Patent Application No. 60 / 381,569 filed May 17, 2002, which makes the entire disclosure as part of the specification of the present application by specifying the source.

An electronic image generator such as a television receiver scans a visible image or a sequence of visible video images on a display screen by electronically sweeping an electromagnetic image beam over the entire screen. For example, in a television receiver, the image beam is a beam of electrons, and the coil creates a linearly increasing magnetic or electric field to sweep the beam.

The optical image generator is similar except that the electromagnetic image beam is mechanically swept across the screen to scan the visible image on the display screen. Alternatively, in the case of a virtual retina display (VRD), the optical image generator scans what is visible directly on the viewer's (s) retinas.

FIG. 1 is a diagram of a conventional optical image display system 10 including an optical image generator 12 and a display screen 14. The image generator 12 includes a generator 16 that produces an optical beam 18, and further includes a scanning assembly 20 that scans the image on the screen 14 with the beam. When the system 10 is a VRD, the scanning assembly 20 scans the image directly on the viewer's (plural) retinas (not shown). The scanning assembly 20 includes a reflector 22 that reciprocates and rotates simultaneously in the horizontal (X) and vertical (Y) dimensions around the pivot arms 24a and 24b and the pivot arms 26a and 26b, respectively. By rotating back and forth, the reflector 22 sweeps the beam 18 in a two-dimensional (XY) raster pattern and produces an image on the screen 14 (or retinas). The scanning assembly 20 includes other components and circuits (not shown) to rotate the reflector 22 and monitor the instantaneous rotation position proportional to the instantaneous position where the beam 18 collides with the screen 14. In an alternative embodiment not shown, the scanning assembly 20 may include two reflectors, one sweeping the beam 18 in the horizontal (X) dimension and the other sweeping the beam in the vertical (Y) dimension. An optical image display system similar to System 10 is disclosed in US Pat. No. 6,140,979 by Gerhard et al., "Scanning Display with Pinch, Timing, and Distortion Correction" and US Pat. No. 5,467,104, "Virtual Retina Display Device" by Fumess et al. These have been incorporated by reference.

With reference to FIGS. 1 to 3, the steps of the optical image display system are described.

Referring to FIG. 1, the image generator 12 starts scanning the image at the initial pixel positions X = 0, Y = 0 and stops scanning the image at the final pixel positions X = n, Y = m, where. n is the number of pixels in the horizontal (X) dimension of the image and m is the number of pixels in the vertical (Y) dimension of the image. Specifically, the beam generator 16 modulates the intensity of the image beam 18 to form the first pixel Z0,0 of the scanned image when the reflector 22 directs the beam to positions X = 0, Y = 0. To do. As the reflector 22 sweeps the beam towards position X = n, Y = m, the generator 16 periodically modulates the intensity of the beam, continuously moving the remaining image pixels, including the final pixel Zn, m. Form. The image generator 12 then begins scanning the next image at positions X = 0, Y = 0 and repeats this procedure for all remaining images.

Referring to FIG. 2, during image scanning, the reflector 22 has a horizontal sweep frequency f in the horizontal (X) dimension._h= 1 / t_hSweep the beam 18 in both directions with a sine wave, where t_hIs the period of the horizontal sine wave. Figure 2 is a plot of this horizontal sine wave, showing the position of beam 18 in the horizontal (X) dimension relative to time, where + corresponds to the right side of screen 14 and-corresponds to the left side. To do. As this plot illustrates, the reflector 22 is like a sine wave around pivot arms 24a and 24b._hAnd therefore sine-wave sweep the beam 18 to the left and right of the screen 14 at the same frequency. The sine wave sweep is bidirectional because the beam 18 is "on" and therefore produces pixels in both the left-to-right (+ X) and right-to-left (-X) horizontal directions. .. Not required, but f_hMay be substantially equal to the resonant frequency of the reflector 22 centered on the arms 24a and 24b. f_hOne of the advantages of designing the reflector 22 to resonate with is that the scanning assembly 20 can drive the reflector in the horizontal (X) dimension with relatively little power.

Referring to FIG. 3, the reflector 22 has a vertical sweep frequency f in the vertical (Y) dimension._v= 1 / t_vSweep the beam 18 in a straight line in one direction with t_vIs the period of the vertical sawtooth wave. Figure 3 is a plot of this sawtooth wave, showing the position of beam 18 in the vertical (Y) dimension in contrast to time, where + corresponds to the bottom of screen 14 and-corresponds to the top. To do. As this plot illustrates, during the vertical scan period V, the scan assembly 20 linearly rotates the reflector 22 from the top position to the bottom position around the pivot arms 26a and 26b, which causes the reflector to rotate. Beam 18 top pixel Z on screen 14_0,0From the bottom of the screen (pixel Z_{n, m}) (-Y direction). In the flyback period FB, the scanning assembly 20 places the reflector 22 in the top position (Z) again._0,0) Quickly (compared to scan period V) to start scanning a new image. As a result, t_v= V + FB, vertical sweep frequency f_v= 1 / (V + FB). Further, in the beam 18, the reflector 22 is at the top of the beam (Z)._0,0) To the bottom (Z)_{n, m}) (-Y direction) is swept "on" only during the scanning period V, and the reflector 22 is in the top position (Z)._0,0Return to) The vertical sweep is unidirectional because it is off during the flyback period FB. One of the advantages of vertically sweeping a beam linearly and unidirectionally is that it is compatible with traditional video equipment that uses the same vertical sweeping technique to produce video images for display.

<p> Unfortunately, sweeping the beam in a unidirectional manner in the vertical (Y) dimension can increase the cost, complexity, size, and power consumption of System 10. Referring to FIG. 3, the vertical sweep sawtooth contains a large number of tunings with a basic vertical sweep frequency fv. For example, when fv = 60Hz, the sawtooth has a significant tuning up to about 3600Hz (60th order tuning, ie 60 × fv). The vibrations brought into the reflector 22 by these harmonics can cause significant errors in the vertical (Y) position of the beam 18. That is, the reflector 22 does not rotate smoothly during vertical scanning and may generate vertical "jitter" or "ripple", which causes the beam 18 to collide with the screen 14 and the beam to be present. Misalignment with the position of the forming pixel Z can occur. One way to reduce or eliminate this error is to include a feedback loop (not shown in FIG. 1) in the scan assembly 20 to smooth the rotation of the reflector 22 during the vertical scan period V. These feedback loops are US patents<u style="single">No. 6,140,979</u>It is disclosed in, which is incorporated by reference. Sorry<u style="single">Na</u>In particular, such feedback loops often include complex circuits that can occupy a large layout area, thus increasing the complexity, size, and cost of the image generator 12. Furthermore, in order to quickly rotate the reflector 22 from the bottom position (Zn, m) to the top position (Z0,0) during the flyback period FB, the scanning assembly 20 often has a large peak current that causes the reflector to rotate. It is necessary to drive an electromagnet (not shown) that rotates 22. Unfortunately, this can increase the power consumed by the image generator 12 and the size of the current drive circuit (not shown) of the scanning assembly, thus further increasing the cost of the image generator. ..</p><p> Another way to reduce or eliminate the ripple error is to generate a drive signal that offsets the non-linearity of the vertical scan. Various approaches can be applied to reduce ripple.</p><p> In one of these approaches, the feedback loop in scan assembly 20 compares the detected angular position around the vertical axis with the ideal waveform. The loop then follows a traditional feedback control approach to generate a drive signal that minimizes error and smoothes the rotation of the reflector during the vertical scan period V.</p><p> Another approach uses a set of scan assembly parameters to build a general analytical or empirical model of the vertical scan assembly for the general features of the scan assembly 20. Then, for a particular scan assembly 20 in use, individual responses are characterized during manufacturing or system startup, the model parameters are refined more accurately, and data representing the particular scan assembly 20 is stored in memory. The scanning assembly then generates a drive signal and minimizes ripple according to the stored model.</p><p> In some cases, such feedback loops and adaptive control systems may contain complex circuits that occupy a large layout area or require special components, thus adding to the complexity of the image generator 12. , Size and cost can be increased.</p>

<p> According to embodiments of the present invention, the scanning assembly sweeps the image beam at a first frequency in the first dimension and bidirectionally at a second frequency lower than the first frequency in the second dimension. Sweep to.</p><p> For example, sweeping the beam in both directions in the vertical dimension can reduce the scanning power by eliminating the flyback period, and reducing the wavenumber in the vertical sweep function can reduce the error in the beam position without a feedback loop. Can be reduced. In addition, the removal of the flyback period causes the image beam to "on" longer, so that the scanned image is often brighter for a constant beam intensity and therefore for a constant image brightness. , The intensity of the image beam, and thus the power, can be reduced proportionally.</p><p> According to another embodiment of the invention, the scanning assembly sweeps the image beam in the first dimension and non-linearly in the second dimension.</p><p> For example, if the beam is sweeped non-linearly in the vertical dimension, the error at the beam position can also be reduced by reducing the wavenumber in the vertical sweep function.</p>

Double sine wave scanning pattern Referring to FIGS. 4-8, a general embodiment according to the invention is a scanning assembly similar to scanning assembly 20 (FIG. 11) that sweeps the image beam in both directions in the vertical (Y) dimension. That is, the image beam is "on" when the scanning assembly sweeps the beam from the top to the bottom of the screen, and is also "on" when the scanning assembly sweeps from the bottom of the screen to the top again. It becomes.

Further referring to FIGS. 4-8, in one embodiment, the scanning assembly is swept bidirectionally in a sinusoidal manner in both the horizontal (X) and vertical (Y) dimensions, but below in connection with FIG. As described, sweep functions other than sinusoidal can be used in either the horizontal or vertical dimensions. For clarity, "double sinusoidal" is used to describe a sinusoidal bidirectional sweep of an image beam in both the horizontal (X) and vertical (Y) dimensions. Since both the horizontal and vertical sweep functions are sinusoidal, the resulting two-dimensional scan pattern is a repeating pattern, such as the Lisaju pattern. For the sake of brevity, the term Lisaju pattern is used herein to refer to a pattern that utilizes sinusoidal motion around two or more axes.

The following variables represent the parameters used to define the double sinusoidal sweep of the image beam according to the embodiments of the present invention.

X (t) = horizontal sweep sine wave as a function of time Y (t) = vertical sweep sine wave as a function of time f_h= Horizontal sweep frequency f_v= Vertical sweep frequency Φ_h= Initial phase of horizontal sweep sine wave (X (t)) Φ_v= Initial phase of vertical sweep sine wave (Y (t)) A = Frequency at which the Lissajous scan pattern formed by horizontal and vertical sweep sine waves appears repeatedly. R = frequency at which the image is scanned / displayed N = number of images scanned / displayed during period 1 / A n_h= Number of horizontal sweep sine wave cycles per period 1 / A n_v= Number of vertical sweep sine wave cycles per period 1 / A p_h= Horizontal resolution of source and scanned images, i.e. horizontal pixels p_v= Vertical resolution of source and scanned images, i.e., number of vertical pixels Δ = maximum width between scan lines in the dimension of minimum sweep frequency These parameters are defined or associated by the following equations. As explained below, some of these equations are not absolute, but merely guidelines. (1) X (t) = (p_h/ 2) sin (2πf_ht + Φ_h) (2) Y (t) = (p_v/ 2) sin (2πf_vt + Φ_v) For example, p_h= 800 and p_vWhen = 600, the range of X (t) is +400 pixels (400 pixels from the center of screen 14 in Fig. 1 to the right) to -400 pixels (400 pixels from the center of the screen to the left), and Y (t). ) Ranges from +300 pixels (300 pixels from the center of the screen to the top) to -300 pixels (300 pixels from the center of the screen to the bottom). (3) N = R / A For example, if the Lisaju pattern appears repeatedly at a speed of A = 1Hz and the image is scanned at a speed of R = 5Hz, then the complete Lisaju pattern is scanned for each period 1 / A N = 5/1 = 5 One image is displayed. (4) f_h= An_h (5) f_v= An_v For example, A = 1Hz and n to complete the Lisaju pattern_h= 9-cycle horizontal sweep frequency f_hIf you need f_h= 1 × 9 = 9Hz. Similarly, the vertical sweep frequency f with nv = 2 cycles to complete the Lisaju pattern._vIf you need f_v= 1 × 2 = 2Hz. Not required, but preferably n_hAnd n_vIs an integer with no common factor other than 1 between them. N as described below in relation to Figure 4._hAnd n_vIf has a common factor other than 1, then f_hAnd f_vIs higher than what should occur at a constant maximum line width Δ.

Combining equations (4) and (5) yields the following equation. (6) f_h/ n_h= f_v/ n_v= A

In addition, as usual (but not always), f_vIs f_hAssuming it is smaller, we have: (7) Δ = (πp_vA) / 2f_h

As explained below in relation to Figures 4-8, most source images assume pixels arranged in a grid pattern, so designers of double sinusoidal image generators will find the results of the scanned image. The values of the above parameters will be selected so that the typical Lisaju pattern "matches" the grid pattern. For example, in a computer-generated source image or a source image captured by a conventional video camera or digital camera, the pixels are arranged in a grid pattern. The Lisaju pattern may differ significantly from the grid pattern, but with proper selection of the values of the above parameters, the quality of the scanned image may approach or be comparable to the quality of the source image. Of course, if the pixels of the source image are placed in the Lisaju pattern, the designer can simply select the parameter values so that the Lisaju scan pattern of the scanned image is the same as the Lisaju pattern of the source image.

FIG. 4 is a plot of an example of one double sinusoidal scanning pattern 40 overlaid on the source image grid pattern 42 according to an embodiment of the present invention. In this example, p_h= 8, p_v= 6, n_h= 9, and n_v= 2. The double sinusoidal scan pattern 40 represents the path through which the image beam is swept horizontally and vertically to scan the image, and thus represents all possible positions for the pixels that make up the scanned image. Conversely, the intersection of grid patterns 42 is the pixels P that make up the source image._{n, m}Identify the position of, where n = P_hAnd m = P_vIs. By convention, P as in this example_hAnd P_vIf is even, the centers C of the scan and the original image match and P in the vertical (Y) dimension, respectively._{n, -1}And P_{n, 1}From ± 0.5 pixels and P in the horizontal (X) dimension_-1,mAnd P_1,mLocated at ± 0.5 pixels from. As a result, in this example, the respective distances ± D from the center C of the source and scanned images to the top 44 and bottom 46, respectively._vIs P_vEqual to / 2 = M / 2 = ± 3 pixels, the respective distance ± Dh to the left 48 and right 50 of the source and scanned image is P_nEqual to / 2 = n / 2 = ± 4 pixels. This is m / 2, which is consistent with equations (1) and (2), and the peak amplitude of the vertical sine wave Y (t) is P._vEqual to / 2 = m / 2 6/2 = 3 pixels, the peak amplitude of the horizontal sine wave X (t) is p_h/ 2 = h / 2 8/2 = equal to 4 pixels. Further, in this example, the image generator (FIG. 17) is assumed to include a scanning assembly in which the reflector or other beam deflector is driven by a double sine wave in the vertical (Y) dimension as described below. ..

Further referring to FIG. 4, in order to design an image generator that scans pattern 40, the designer first determines the desired maximum line width Δ. As described above and illustrated in FIG. 4, Δ is the maximum width in the vertical (Y) dimension between the two adjacent horizontal lines of the scan pattern 40. Empirical studies of image quality show that Δ-1 may be the preferred choice. Therefore, by setting Δ-1 to satisfy this guideline, f from the above equation (7)_hThe following equation is derived. (8) fh (πP_vA) / 2

Then A can be determined. For example, assume that the source image is a video image with a display speed of R = 30 Hz (30 images per second) and the image generator (FIG. 17) scans one image for each Lisaju pattern (N = 1). Therefore, according to Eq. (3), A = 30Hz.

Next, the designer, N_vSelect. For example, the designer is N_vSuppose you want = 2 (two vertical sweep cycles for each Lisaju pattern).

Next, the designer finds out from equation (5) to f._vTo calculate. In this example, A = 30Hz and n_v= 2 and f_v= 60Hz. f_vCan be any frequency that fits the scanning assembly, but for image quality purposes -50Hz f_v -75Hz or f_vIt has been empirically determined to be&gt; 1500Hz.

Next, the designer finds out from equation (8) to f._hCalculate the minimum value of. In this example P_v= 6 and A = 30Hz, f_h (π6 × 30) / 2 -28 2.60Hz.

Next, the designer preferably satisfies Eq. (8) substantially, and h other than 1._vN that do not have a common factor with_hGenerate an integer for f_hSelect the lowest value of. From equation (6), f_hIf you select = 270Hz, n_h= 9 occurs, in this case n_vThere is no common integer factor with. f_h= 270Hz &lt;282.60Hz, but Equation (7) yields a maximum line width Δ = 1.05 pixels that is within 5% of the desired maximum line width of 1 pixel. Therefore, f_h= 270Hz substantially satisfies Eq. (8). Of course, the designer is even lower when producing scanned images of acceptable quality._hYou can select the value of. As an alternative, the designer n_hHigher f, such as 330Hz to generate = 11 and Δ &lt;1_hYou may choose the value of. However, scanning assemblies (Figure 17) usually have a low horizontal frequency f._hPower consumption is reduced.

Other embodiments of the above design method are conceivable. For example, the designer may perform the steps of the design procedure in a different order than that described above. In addition, n_hAnd n_vMay have a common factor other than 1. However, this is simply a high frequency f with no reduction in the maximum line width Δ._hAnd f_vJust generate. For example, the designer is n_h= 18 and n_vF such that = 4_h= 540 and f_h= 120 can be selected. However, these high frequencies are simply f_h= 270 and f_hIt just retraces Lisaju pattern 40 twice as fast as = 60. Therefore, as mentioned above, n has no common factor other than 1._hAnd n_vBy selecting, the minimum Δ is provided for the frequency used. In addition, n_hAnd n_vOne or both may be non-integers. However, this may cause the Lisaju pattern to start and end at different points on the display screen for each blanking interval (1 / A), thus "rolling" the pattern unless additional processing is applied. is there. Such rolls can adversely affect the quality of the scanned image. In addition, f in the above example_h&gt;&gt; f_vIn, the designer<img file="JP4379331B2_D0001.tif" />, F_h&gt; f_v, Or fv &gt;&gt; f_hCan be selected. f_v&gt;&gt; f_hIf, the designer puts p in equation (7)._hP_vAs an alternative to f_hF_vShould be a substitute for, f_v= f_hIf, the designer should use equation (7) and the equivalent equation in the vertical to guarantee the desired maximum line width Δ in both the horizontal (X) and vertical (Y) dimensions. .. Further, the horizontal and vertical sweep functions X (t) and Y (t) may be other than a sine wave. An example of the non-sinusoidal function Y (t) is described below in connection with FIG.

Although the above rolls can degrade image quality or increase the complexity of data processing, such an approach may be desirable in some cases. For example, in imaging or low resolution applications, non-integer ratios can allow greater flexibility in scanner design or improve addressability, while usually increasing the risk of image artifacts.

With reference to FIGS. 4, 5A, and 5B, the designer then generates the theoretical minimum value of the maximum line width Δ calculated according to equation (7), the horizontal sine waves of equations (1) and (2). Determine a suitable phase relationship between X (t) and the vertical sine wave Y (t). FIG. 5A is a plot of X (t) and Y (t) over time in one of the possible and preferred phase relationships that generate the Lissajous scan pattern 42 of FIG. 4, and FIG. 5B produces the pattern 42. A plot of X (t) and Y (t) over time in another possible and preferred phase relationship.

In general, as described below in relation to FIGS. 6-8, a suitable phase relationship occurs when there is a minimal correlation between the peaks of X (t) and Y (t). Specifically, a preferred phase relationship exists between X (t) and Y (t) when both of the following equations are satisfied at the same time. (9) 2πf_vt + Φ_v0(All phases of Y (t)) = ± π / 2 (10) k = 0,1, ... (2n_vAbout -1) 2πf_ht + Φ_h0(All phases of X (t)) =-π / 2 + (π / n)_v) [K + 1/2] As an inevitable consequence of equations (9) and (10), a suitable phase relationship exists between X (t) and Y (t) even when both of the following equations are satisfied at the same time. (11) 2πf_ht + Φ_h0(All phases of X (t)) = ± π / 2 (12) k = 0,1, ... (2n_hAbout -1) 2πf_vt + Φ_v0(All phases of Y (t)) =-π / 2 + (π / n)_h) [K + 1/2] Since fv fh, the momentary difference between all phases of X (t) and Y (t) changes over time. Therefore, Eq. (10) defines the permissible phase of X (t) when the phase of Y (t) has a constant value-± π / 2 in this example-and similarly Eq. (12). ) Defines the permissible phase of X (t) when the phase of X (t) has a constant value-also ± π / 2 in this example. Furthermore, there is a permissible phase of X (t) when Y (t) has a constant phase other than ± π / 2, or Y when X (t) has a constant phase other than ± π / 2. It is also possible to derive other equations that produce the permissible phase of (t). However, regardless of which equation was used, they all define the same preferred phase relationships (groups) illustrated in Figures 5A and 5B.

Further referring to FIGS. 4, 5A, and 5B, Eq. (12) is solved for X (t) and Y (t) in FIGS. 5A and 5B in order to illustrate the concept of such a suitable phase relationship. In n_h= 9. Specifically, according to Eq. (12), the preferred phase relationship is shown in Table 1 for all phases of Y (t) for each peak of X (t) (phase = ± π / 2). It exists when it is done. table 1 All phases of k Y (t) 4 0π 5 π / 9 6 2π / 9 7 3π / 9 8 4π / 9 9 5π / 9 10 6π / 9 11 7π / 9 12 8π / 9 13 π 14 10π / 9 15 11 π / 9 16 12π / 9 17 13 π / 9 0 14 π / 9 1 15π / 9 2 16π / 9 3 17 π / 9

As illustrated in FIGS. 5A and 5B, for the peak of X (t), the entire phase of Y (t) is actually equal to one of the values in Table 1. More specifically, FIG. 5A shows that the first preferred phase relationship exists when the total phase of Y (t) is equal to each odd multiple of π / 9 for each phase of X (t). 5A shows that a second preferred phase relationship exists when the total phase of Y (t) is equal to each even multiple of π / 9 for each phase of X (t). Is illustrated. Both the first and second preferred phase relationships give rise to scan pattern 40 (FIG. 4), but the scan assembly (FIG. 17) is in the first direction for the first preferred phase relationship and second. The pattern 40 is scanned by sweeping the image beam in the opposite direction for the preferred phase relationship of. However, since the sweep direction usually does not affect the quality of the scanned image, any suitable phase relationship will usually produce an acceptable scanned image.

With reference to FIGS. 6-8, the undesired effect of shifting the phase relationship between X (t) and Y (t) from a favorable phase relationship to the worst case or to the worst case. Explained. Specifically, by shifting the phase relationship, the maximum line width Δ (FIGS. 6 and 7) increases from the theoretical minimum value (FIG. 4).

FIG. 6 shows the double sinusoidal scanning pattern of FIG. 4 when the phase relationship between X (t) and Y (t) is unfavorable and therefore the maximum line width Δ is greater than the theoretical minimum (FIG. 4). There are 40 plots. The scan pattern 40 has two components. During the first cycle of the vertical sweep function Y (t), the scan assembly (FIG. 17) sweeps the first component and during the second cycle of the vertical sweep function Y (t), the scan assembly (FIG. 17). ) Sweeps the second component spatially offset from the first component. As the phase relationship between X (t) and Y (t) begins to shift from the preferred one, the first and second components effectively move towards each other, and thus the maximum line width Δ. To increase. A suitable phase relationship may be considered optimal, but the system may be operated away from this optimal condition if other system considerations, such as cost, result in desirable behavior. The increased maximum line width Δ can bring in image artifacts, which can be tolerated in some applications.

FIG. 7 is a plot of the double sinusoidal scan pattern 40 of FIG. 4 when the phase relationship between X (t) and Y (t) is the worst case and therefore the maximum line width Δ has the maximum value. Is. Due to the worst-case phase relationship, the first and second components of pattern 40 are effectively merged so that they overlap each other. During the first cycle of the vertical sweep function Y (t), the scanning assembly (FIG. 17) sweeps the first component from top left to top right of pattern 40. In addition, during the second cycle of Y (t), the scanning assembly sweeps the second component by retracing the first component from top right to top left of pattern 40. That is, the scanning assembly effectively sweeps the pattern 40 in one direction during the first cycle of Y (t) and retraces the pattern in the other direction during the second cycle of Y (t). Since the two components overlap, the resulting worst-case Lisaju pattern 40 is n_v= 1 and n_hIt is equal to the pattern of a single component with = 4.5, which is the theoretical minimum value shown in FIG. 4, and a maximum line width Δ = 2, which is twice the theoretical minimum value of -1 pixel.

FIG. 8 is a plot of X (t) and Y (t) for time in the phase relationship of the first worst case where the Lisaju pattern 40 of FIG. 7 occurs. The worst-case phase relationship occurs when there is a maximum correlation between the peaks of X (t) and Y (t). More specifically, the worst-case phase relationship occurs when the X (t) peak periodically coincides with the Y (t) peak. For example, at t1 and t2, the positive peak of Y (t) coincides with the negative and positive peaks of X (t), respectively, generating the first worst-case phase relationship. These peak coincidences correspond to the upper left and upper right of pattern 40, respectively, where the scanning assembly effectively "bounces" the image beam back and forth between the upper left and upper right "corners" of pattern 40.

Referring to FIGS. 7 and 8, the phase relationship of the second worst case is that the negative peak of Y (t) coincides with the negative and positive peaks of X (t), respectively, and therefore for pattern 40. Occurs when an upside-down Lissajous scanning pattern occurs.

Therefore, referring to FIGS. 4-8, the preferred phase relationships of X (t) and Y (t) are exactly intermediate between the two worst-case phase relationships, respectively, and equations (9) to (9) to 8 In (12), such an intermediate point occurs. Specifically, n_h= 9 and n_vWhen = 2, in the first and second worst case phase relationships, the total phase of Y (t) is an odd number of π / 18 for each peak (± π / 2) of X (t). It is a multiple (see FIG. 8), and in the first and second preferred phase relationships, the entire phase of Y (t) is even π / 18 for each peak of X (t) according to equation (12). It will be a multiple. As a result, the even multiples of π / 18 are exactly in the middle between the odd multiples of π / 18, so the two preferred phase relationships are exactly in the middle between the two worst case phase relationships. Source image switching speed f for bidirectional vertical sweep_sVertical sweep frequency f_vOffset from

As described below in relation to FIGS. 9 and 10, when the video image is scanned in a temporal sequence different from the temporal sequence of the corresponding source image, the viewer (not shown) is a fake ghost object. Etc. can be perceived. More specifically, the speed at which the image beam is switched from one source image to another f_sIs the vertical sweep frequency f_vWhen synchronized with, the human eye can perceive these artifacts in bidirectionally scanned video images in the vertical dimension. The viewer perceives a true ghost object when he sees an object that moves faster than the duration of the image in his eye. Specifically, when the eye perceives an object, the image of the object persists for a period of time, even after the object moves from the position originally perceived by the eye, which is approximately a few milliseconds. .. When an object moves fast enough, the eye perceives "blurring", which is equivalent to perceiving the object in multiple positions at the same time. This phenomenon can be observed by trying to see the finger while moving the finger back and forth quickly. "Ghost object" is just another name for this blur, and refers to the perception of an object by the eye at one or more positions that the object does not occupy. A fake ghost object is a ghost object that the viewer perceives in a sequence of video images, but does not perceive when looking directly at the object. Fake ghost objects are usually caused by errors introduced when capturing or scanning an image.

FIG. 9 is a diagram of three consecutive scanned video images 50a-50c when the viewer (not shown) can perceive fake ghost objects 52 and 54 by bidirectional scanning of the images in the vertical dimension.

The double sinusoidal scan images 50a to 50c correspond to the respective source video images S1 to S3 and represent the motion of the ball 56 and the toy car 58. That is, the image 50a is reproduced by the double sine wave scanning of S1, the image 50b is the reproduction by the double sine wave scanning of S2, and the image 50c is the reproduction by the double sine wave scanning of S3. The image generator (FIG. 17) may receive pixels of the source image S from the image buffer (FIG. 17) or in real time via a stream of video data. The source images S1 to S3 are captured from one source image to the next source image so that a known time elapses between the captures of the moving objects. Specifically, when the source image S is captured by conventional raster scanning or optical integration techniques, the elapsed time between captures of pixels at the same relative position in successive source images S is substantially constant. For example, if the source images S1 to S3 are captured at a speed of 30 Hz (1/30 second per image) in this way, the elapsed time between pixel P1 of S1 and pixel P2 of S2 is 1/30 second. And so is the elapsed time between pixel P3 in S2 and pixel P4 in S4. As a result, the relative distance between the positions of the ball 56 in the source images S1 and S2 represents the movement of the ball for about 1/30 second that has elapsed during the capture of the ball at these two positions. Similarly, the relative distance between the positions of the car 58 in the source images S2 and S3 represents the movement of the car for about 1/30 seconds that has elapsed during the capture of the car at the two positions.

However, an image generator (FIG. 17) that scans image 50 in both directions in the vertical dimension by repeatedly switching from one source image S to the next at the same relative position of image 50 is very quick. In addition, it may cause a continuous occurrence of moving objects, such that the eye perceives a fake ghost object at this relative position. In the example of FIG. 9, the image generator switches the image beam from the source image S1 to the source image S2 at the top of the scanned image 50b, switches the beam from S2 to S3 at the bottom of the image 50b, and follows this switching pattern. F to repeat for images S and 50_s= 2f_vWill be. As a result, f_vAssuming that = 15Hz, each image 50 is scanned in 1/30 seconds, and the ball 56 is located about 1/8 below the top of image 50, the generation of ball 56 in image 50a and the ball in image 50b. The time t elapsed between generations is about 1/4 x 1/30 = 1/120 seconds, which is significantly shorter than the actual 1/30 seconds between the positions of the balls in the source images S1 and S2. Therefore, if T is shorter than the duration in the human eye, looking at the scanned image 50b, the ball 56 is perceived to be co-existing at positions S1 and S2, where the persistence of the ball from image 50a is perceived. Generates a fake ghost object 52 in image 50b. Observing this in another way and exemplifying it using the above example, vertical bidirectional scanning moved the ball between positions at 50a and 50b in 1/120 seconds instead of the actual 1/30 seconds. By "fooling" the viewer to perceive, it effectively increases the perceived speed of the ball 56 by a factor of four. Even if the ball 56 moves fast enough to produce a true ghost object, the above phenomenon still produces a fake ghost object 52 by exacerbating the true ghost object. Similarly, if the time elapsed between the generations of the vehicle 58 in images 50b and 50c is shorter than the duration of the human eye, the viewer will see the scanned images 50c and will co-exist at positions 50b and 50c. Perceive the car 58 in. As a result, the persistent car perception from image 50b gives rise to the fake ghost object 54 in image 50c.

Further referring to FIG. 9, one way to reduce or eliminate the perception of fake ghost objects is to scan image 50a in only one vertical direction. For example, instead of scanning image 50a from bottom to top in the first half of the first vertical sweep cycle and image 50b from top to bottom in the second half of the first cycle, a scanning assembly (Figure 17). Scans image 50a from bottom to top in the first half of the first vertical cycle, deactivates the image beam in the second half of the first cycle, and then scans image 50b in the first half of the second vertical cycle. It is possible to scan from the bottom to the top. Unless the fv is significantly higher than the frequency at which the images S1 through S3 are captured, this unidirectional vertical scan effectively eliminates fake ghost objects.

Seeing Figure 10, another technique for reducing or eliminating fake ghost objects is f._vSo that the image generator (Fig. 17) does not frequently switch from one source image S to another at the same relative position of the scanned image 50, so that it is out of sync with f._sIs to select.

For example, f_s= 8f_vIf 5 / 5, the image generator (FIG. 17) first generates an image beam from the pixels of the source image S1 as it scans the image 50a from the bottom 60a to the top 62a.

The image generator then starts scanning image 50b from the top 62b, but is located 1/4 below image 50b and is the source up to line 64b, which is 5/4 image 50 away from bottom 60a. Do not start generating beams from the pixels of image S2. That is, since the image generator continues to generate the image beam from the source image S1 up to the line 64b of the image 50b, the upper 1/4 of the image b becomes the same as the upper 1/4 of the image 50a.

The image generator then completes scanning the image 50b below line 64b while generating an image beam from the pixels of the source image S2.

The image generator then starts scanning the image 50c from the bottom 60c, but generates a beam from line 64b to line 66c, which is located 1/2 above image 50c and 5/4 image 50. Do not switch to pixels in the source image S3. That is, since the image generator continues to generate the image beam from the source image S2 up to the line 66c of the image 50c, the lower 1/2 of the image 50c is the same as the lower 1/2 of the image 50b.

The image generator then completes scanning the image 50c above line 66c while generating an image beam from the pixels of the source image S3.

The image generator then begins scanning image 50d from the top 62d, but generates a beam from line 66c to line 68d, located 3/4 below image 50d and 5/4 image 50. Do not switch to pixels in the source image S4. That is, since the image generator continues to generate the image beam from the source image S3 up to the line 68d of the image 50d, the upper 1/2 of the image 50d is the same as the upper 1/2 of the image 50c.

The image generator then completes scanning the image 50d below line 68d while generating an image beam from the pixels of the source image S4.

The image generator then starts scanning the image 50e from the bottom 62e, but does not switch the beam to the pixels of the source image S5 up to the top 62e of the image 50e.

The image generator continues in this way, periodically repeating the switching lines 60, 62, 64, 66, and 68. However, the frequency of switching on any single line is low enough to reduce or eliminate the perception of fake ghost objects.

This technique can generate a fake ghost object on the switching line, but since the switching line effectively moves every 50 scans so that the frequency at which a particular line is switched is relatively low, the fake ghost object is It has been empirically determined that it is not very noticeable or perceived. The occurrence of fake ghost objects can be further reduced if the duration of the particular switching line repetition is longer than the duration in the human eye. For example, if the time between switching the source image at line 66 and the next switch at line 66 is longer than the duration in the human eye, the viewer perceives a fake ghost object less near line 66. Will not be.

Furthermore, f_s= 8f_vI explained the example of / 5, but f_sAnd f_vThere are other relationships with and that reduce / eliminate fake ghost objects. The optimal relationship between fs and fv and other artifacts is f_sAnd f_vIt depends on the application and the actual value of, and is therefore often determined on an ad hoc basis. Modulation of image beam intensity relative to beam position

With reference to FIG. 11, in a sinusoidal sweep of an image beam, one part of the scanned image may appear brighter than the other, unless corrected.

FIG. 11 is a Lisaju pattern 70 in which the resulting scanned image may have non-uniform brightness. As described above in connection with FIGS. 4-8, the image generator (FIG. 17) is a sinusoidal sweep of the image beam in both the horizontal (X) and vertical (Y) dimensions. Scan pattern 70. Due to the sinusoidal sweep function, the lines of pattern 70 are more precise in the top region 72, bottom region 74, and side regions 76 and 78 because they are closer to each other than the lines in central region 80. become. More specifically, the top and bottom regions 72 and 74 correspond to the peaks of the vertical sinusoidal sweep function Y (t) (see Equation (2) and FIGS. 5A and 5B), so that the beam is Compared to the movement in the central region 80, these regions move slower in the vertical (Y) dimension. Therefore, the image generator is the most suitable because the beam collides with each area unit longer in the uppermost and lowermost areas 72 and 74 than in the case where the beam collides with each area unit of the same degree in the central region 80. In the top and bottom regions, more lines are swept per unit area, thus forming more pixels in the scanned image. As a result, in the top 72 and 74 regions, the pixels become denser, so that these regions appear brighter than the central region 80 if the image beam has a uniform maximum intensity across pattern 70. Similarly, the left 76 and right 78 regions correspond to the peaks of the horizontal sinusoidal sweep function X (t) (see Equation (1) and Figures 5A and 5B), so that the beam is horizontal in these regions. Moves slowly in the X) dimension. Therefore, in the 76 on the left side and the 78 on the right side, the pixels become denser, so that if the beam has a uniform intensity throughout the pattern 70, these areas will appear brighter than the central area 80.

The traditional method of equalizing the brightness of a scanned image when the beam is sinusoidally swept in the horizontal (X) dimension is to modulate the beam intensity in proportion to the instantaneous sweep rate in the horizontal (X) dimension. Is. Therefore, in the side region of the scanned image where the beam velocity is slow, the beam intensity is proportionally low, and in the central region where the beam velocity is high, the beam intensity is proportionally high. More specifically, the horizontal sweep function X (t) = sin (2πf)_ht + Φ_h) Means the horizontal position of the beam, so if Imax is used to indicate the maximum instantaneous intensity of the beam, the modulated instantaneous intensity of the beam will be I._max(Instantaneous horizontal velocity) / (Maximum horizontal velocity) = I max × (d / dt sin (2πf)_ht + Φ_h))) / max (d / dt sin (2πf)_ht + Φ_h)) Equal to, therefore, obtained by (13) I (Maximum modulation instantaneous beam intensity) = I_max× cos (2πf_ht + Φ_h) / 1 This horizontal modulation technique is further described in US Pat. No. 6,445,362 to Tegreene, "Scanning Beam Display with Change Correction," which is incorporated by reference. However, the vertical sweep frequency f_vIs the horizontal sweep frequency f_hIntuitively, modulation of beam intensity by vertical sweep rate does not appear to provide the desired results if it is significantly lower than.

Further referring to FIG. 11, in one embodiment of the invention, the image generator (FIG. 17) modulates the beam intensity in proportion to the instantaneous sweep velocity in both the horizontal (X) and vertical (Y) dimensions. This makes the brightness of the scanned image even more uniform. The inventor has determined that the desired result is obtained by modulating the beam intensity according to the vertical sweep rate. Therefore, in the top, bottom, and side regions 72, 74, 76, and 78 of the low beam velocity scan image, the beam intensity is proportionally low, and in the central region 80, where the beam velocity is high, the beam intensity. Is proportionally higher. Specifically, the vertical sweep function Y (t) = sin (2πf)_vt + Φ_v) Means the vertical position of the beam, so if Imax is used to indicate the maximum instantaneous intensity of the beam, the maximum modulation instantaneous intensity I of the beam is obtained by: (14) I = I_max× cos (2πf_ht + Φ_h) × cos (2πf_vt + Φ_v) An alternative embodiment is to modulate the beam intensity only in proportion to the vertical sweep rate as follows: (15) I = I_max× cos (2πf_vt + Φ_v) From the sine wave sweep functions X (t) and Y (t) of equations (1) and (2) to cos (2πf)_vt + Φ_v) And / or cos (2πf_ht + Φ_h), And the conventional circuit that can modulate the beam intensity accordingly is relatively simple, and therefore this modulation technique is relatively easy to implement.

Referring to FIGS. 11 and 12, in another embodiment of the invention, the image generator (FIG. 17) sweeps the image beam more linearly in the vertical (Y) dimension, resulting in non-uniform brightness of the scanned image. Improve sex.

Figure 12 shows n_v= 2, n_h= 9, p_v= 6, and p_hA plot of the horizontal and vertical sweep functions X (t) and Y (t) with respect to time, where = 8, but this embodiment of the invention is of the other n._v, N_h, P_v, And p_hCan also be used with the value of. The horizontal sweep function X (t) is a sinusoid as described above in relation to equation (1) and FIGS. 4-8, whereas the vertical sweep function Y (t) is a pseudo with rounded peaks. It is a triangular wave. By making the slope of the vertical sweep function Y (t) more linear, the image generator (Figure 17) sweeps the beam at a more constant velocity in the vertical (Y) dimension, and therefore the line density, and therefore Further, the brightness is made more uniform in the top, bottom, and central regions 72, 74, and 80 of pattern 70 (FIG. 11). More specifically, an embodiment of this vertical sweep function Y (t) is obtained by the following equation. (16) Y (t) = (1-u) (P_v/ 2) sin (2πf_vt + Φ_v) + U (P_v/ 2) sin (2π3f_vt + Φ_v) Where u is an empirically determined scale factor. From equation (16), f_vIt can be confirmed that by adding the third-order wave of Eq. (2) to the sine wave Y (t) of Eq. (2), a more linear slope of the vertical sweep function Y (t) can be obtained. Furthermore, when an additional odd-numbered wave above the third-order wave is added, the slope becomes more linear by bringing Y (t) closer to the triangular wave. In addition, as described below, an image generator was designed to sweep the beam vertically according to equation (16), and X (t) in equation (1) according to the concepts described above in relation to FIGS. 4-8. ) And Y (t) in Eq. (16) can be calculated.

With reference to FIGS. 11 and 12, other embodiments that improve the brightness non-uniformity of the scanned image are conceivable. For example, the beam can be swept vertically according to equation (15) and the intensity of the beam can be modulated in proportion to the horizontal sweep speed, the vertical sweep speed, or both the horizontal and vertical sweep speeds. Further, the beam intensity can be modulated in proportion to the linear function of the beam position or as a function of the scanning angle of the beam instead of being proportional to the sweep rate which is the (derivative of the position and scanning angle) of the beam.

With reference to FIG. 12, another advantage of making the linear density of the scan pattern more uniform, such as pattern 70 (FIG. 11), is that the maximum line width Δ is reduced and is therefore desirable with a lower horizontal sweep frequency fh. The value of Δ can be achieved. The following equation is a more general form of equation (7). (17) Δ = (maximum vertical beam velocity) / 2f_hn_v

Where f_v&lt;n_vWill be. Therefore, by reducing the maximum vertical beam velocity proportional to the maximum slope of the vertical sweep function Y (t) (ie, the maximum value of the time derivative), f_hCan be proportionally reduced, and Δ can be maintained at a desired value. Since the maximum slope of the pseudo-triangle wave in Fig. 12 is smaller than the maximum slope of the sine wave (Fig. 5A and 5B), by using the pseudo-triangle wave for Y (t), f without increasing Δ._hCan be reduced.

Further referring to FIG. 12 and Eq. (16) again, the phase and frequency relationship described above in relation to FIGS. 4 to 8 is as follows:_vA vertical sweep function Y (t) containing one or more of the tones of is determined according to an embodiment of the present invention. Specifically, equations (5), (6), (9), and (12) are the fundamental frequencies f of any of these functions Y (t)._vIt is effective in. Furthermore, Eq. (12) tunes the possible resulting phase f._v/ f_vJust multiply by f_vCan be modified for each wave adjustment. For example, the equation of the third-order wave phase corresponding to equations (11) and (12) is as follows (equation (11) does not change). (11) 2πf_ht + Φ_h0(All phases of X (t)) = ± π / 2 (18) k = 0,1, ... (2n_hAbout -1) 2π3f_vt + Φ_v0(All phases of third-order tuning of Y (t)) = 3 (π / 2 + (π / n)_h) [k + 1/2])

As a result, an image generator using the multi-wave vertical sweep function Y (t) can be designed according to the procedure described above in connection with FIGS. 4-8. In addition, the same principle can be used to design an image generator that uses the multi-wave horizontal sweep function X (t). Interpolation of scan pixel intensity from source pixel

Referring to FIGS. 13-15, the position of the scan pixel usually does not coincide with the position of the source pixel because the sinusoidal scan pattern usually does not intersect the position of the source pixel from the source image. As a result, the image generator (FIG. 17) may interpolate the intensity of the scanning pixels from the intensity of the source pixels to improve the quality of the scanned image.

FIG. 13 is a plot of the double sinusoidal scan pattern 40 and grid pattern of FIG. 4, which forms scan pixels Z on vertical grid lines and intensifies from vertically adjacent source pixels P according to an embodiment of the invention. The method of interpolating is illustrated.

To locate the scanning pixels Z that coincide with the vertical lines of grid pattern 42, the image generator (FIG. 17) generates a non-linear pixel clock that indicates when the image beam intersects the vertical grid lines. Since the horizontal sweep function X (t) is non-linear-here, a sine wave according to equation (5) -from the time the beam crosses the vertical grid line to the time it crosses the closely adjacent vertical grid line. The time varies from grid line to grid line. For example, the beam is grid lines 3 and 4 (pixel Z)_{4, y}And Z_{3, y}When moving between), the beam is grid lines -1 and 1 (pixel Z)_{1, y}And Z-_{1, y}) Takes longer than moving between. This means that in the horizontal (X) dimension, near the sides of pattern 40-the sides correspond to the peaks of the horizontal sine wave-the central part-the central part corresponds to the zero intersection of the horizontal sine waves. This is because the beam moves at a slower speed than near. Therefore, the image generator generates a pixel clock so that the instantaneous period of the pixel clock is proportional to the horizontal velocity of the beam. As a result, the pixel clock "knocks" whenever the beam intersects the vertical grid lines (or a given offset time before this intersection), regardless of the horizontal position of the beam. Techniques for generating such pixel clocks are disclosed in previously incorporated US Pat. No. 6,140,979.

Since the scanning pixel Z coincides with the vertical line of the grid pattern 42, the image generator interpolates the intensity of each pixel Z from the source pixels P directly above and below the pixel Z on the same vertical grid line. For example, the image generator is the source pixel P_1,1And P_1,-1From the intensity of pixel Z_{1, y}Interpolates the intensity of. In one embodiment, the image generator Z_{1, y}Strength IZ_{1, y}To calculate (19) IZ_{1, y}= αIP_1,1+ (1-α) IP_1,-1 Where α is P_1,-1And Z_{1, y}The absolute value of the vertical distance between and (1-α) is P_1,1And Z_{1, y}Absolute value of the vertical distance between and IP_1,-1And IP_1,1Is the source period P₁, -1 and P_1,1The strength of each. The image generator typically extracts the intensity of pixels P from a buffer (FIG. 17) that stores the corresponding source image. Alternatively, the image generator may use other conventional interpolation algorithms.

As explained in the previous paragraph, to interpolate the intensity of scan pixel Z from adjacent source pixels P, the image generator can determine which pixel P to use for interpolation with grid 42. Track the relative position of the image beam. A technique for tracking the position of an image beam is described below.

Further referring to FIG. 13, one method of tracking the horizontal position of the image beam is to clock the horizontal position counter with a non-linear pixel clock. For example, when the beam is started at the left edge of pattern 40, the clock can store zero as the initial count. Then the beam moves to the right and the vertical grid line p_hAt the intersection of = -4, the pixel clock "steps" and increments the count by one, thus indicating the first pixel in the horizontal dimension. This increment causes the beam to have vertical grid lines p_hContinues on each vertical grid line until the pixel clock increments the count to 8 when it crosses = 4. Next, the vertical grid line p on the way the beam returns from the right edge of pattern 40._hAt the intersection of = 3, the pixel clock "steps" and decrements the count by one, thus indicating the seventh pixel in the horizontal direction. This decrement continues on each vertical grid line until the pixel clock decrements the count to 0 again. This increment / decrement cycle is then repeated in each subsequent cycle of the horizontal sweep function X (t).

The image generator can track the vertical position of the image beam in a similar fashion by generating a non-linear vertical pixel clock and internally clocking the vertical position counter. To provide a measure of α, the frequency of the nonlinear vertical pixel clock can be increased by a scale factor. For example, increasing the frequency by a factor of 10 provides 10 clock "steps" between each pair of pixels in the vertical dimension, thus providing α with a resolution of 0.1 pixels.

Another technique for tracking the horizontal and vertical positions of the image beam is described below in connection with FIG. Other techniques are available, but are omitted for brevity.

Referring to FIG. 14, generating a non-linear pixel clock often requires a relatively large and complex circuit, so the image generator (FIG. 17) is a linear pixel clock (a clock with a constant period). May be used to complement the intensity of scan pixel Z, as described below.

FIG. 14 is a plot of one area of the grid pattern 42 of FIG. 13 and scanning pixels Z having arbitrary positions within this grid area, according to an embodiment of the present invention. The linear pixel clock does not force the scan pixel Z to match the vertical lines of grid pattern 42, so pixel Z is any position within the grid area x + β (horizontal component), y + α (vertical). Can have components). Therefore, the image generator (Figure 17) follows the following traditional bilinear interpolation equation, and from the intensities of the four surrounding source pixels, Z_{x + β, y + α}Interpolates the intensity IZ of. (20) IZ = (1-α) [(1-β) IP_{x, y}+ βIP_{x + 1, y}] + α [(1-β) IP_{x, y + 1}+ βIP_{x + 1, y + 1}] Equation (20) is pixel Z_{x + β, y + x}The scanning assembly (Fig. 17) is effective in forming the image regardless of the direction in which the image beam is being swept. Alternatively, the image generator follows these four source pixels P, a subset of these four source pixels, other source pixels, or another interpolation algorithm that uses a combination of these source pixels and other source pixels. Strength IZ may be complemented.

FIG. 15 is a block diagram of a position tracking and interpolation circuit 100 that can operate to track the horizontal and vertical positions x + β and y + α of a double sinusoidal sweep image beam according to an embodiment of the present invention. The circuit 100 interpolates with the pixel clock circuit 102, the horizontal and vertical phase accumulators 104 and 106, the horizontal and vertical position accumulators 108 and 110, the memory 112, and the horizontal and vertical position converters 114 and 116. Includes vessel 118. As described below, the pixel clock circuit 102 produces a linear pixel clock with a constant clock period. The phase accumulators 104 and 106 track the phases of the horizontal and vertical sweep functions X (t) and Y (t) (Equations (1) and (2)), respectively. The position accumulators 108 and 110 calculate the horizontal and vertical positions of the image beam from the horizontal and vertical phases and the sweep function trajectory approximation from the memory 112, respectively. The converters 114 and 116 convert the horizontal and vertical positions to the coordinates of the source image grid pattern as shown in pattern 42 of FIG. 13, respectively, and the interpolator 118 is from the converted horizontal and vertical positions and their respective source pixels P. , Scanning pixel Z_{x + β, y + α}Calculate the intensity of.

The clock circuit 102 generates a linear pixel clock having a frequency of fp according to the following equation. (21) f_p= Mf_h Where M = 2p_hIs. For example, referring to FIG. 13, the phase of the horizontal sweep function X (t) is equal to -π / 2 on the left side of the scan pattern 40 and + π / 2 on the right side, P._hSuppose = 8. The image generator (Figure 17) sweeps eight pixels Z during a left-to-right sweep as it sweeps the image beam throughout a 2π radian full horizontal cycle (from left to right and back to left). Generate and generate another eight pixels Z during the right-to-left sweep. As mentioned above, since each "step" of the pixel clock identifies the moment when each pixel Z is generated, the pixel clock contains 16 "steps" per horizontal cycle, and therefore 16f in this example._hEqual to (16 times the horizontal sweep frequency).

The horizontal and vertical phase accumulators 104 and 106 track all phases θ and Ψ of the horizontal and vertical sweep functions X (t) and Y (t), respectively, according to the following equations: (22) θ_n= θ_n-1+ 2π / M (23) Ψ_n= Ψ_n-1+ (n_v/ n_h) 2π / M Here, π represents the current step of the pixel clock, and n-1 represents the immediately preceding step. For example, if the horizontal and vertical sweep functions X (t) and Y (t) are sine waves according to equations (1) and (2): (24) θ = 2πf_h+ Φ_h (25) Ψ = 2πf_v+ Φ_v Since the phase of the sine wave increases linearly with time, the horizontal phase θ increases by the same amount of 2π / M for each step of the pixel clock. For example, for M = 16, the horizontal phase θ is incremented by π / 8 radians for each step and therefore the horizontal sweep frequency f as described above._hComplete a complete rotation of 2π every 16 "steps" that correspond to one cycle. Furthermore, f_v= f_hn_v/ n_hSince (Equation (6)), the vertical phase Ψ is n of θ._v/ n_hOnly doubles. For example, n_v= 2, n_hIf = 9 and M = 16, Ψ increments by (2/9) × π / 8 = π / 36 radians for each step, and therefore every 72 steps of the pixel clock. That is, the horizontal sweep frequency f_hRepeat a complete rotation of 2π every four and a half cycle of. This is consistent with equation (6) and FIGS. 5A and 5B. Further, in one embodiment, θ_nAnd Ψ_nOverflows to zero when it reaches 2π.

With reference to FIGS. 15 and 16, the horizontal and vertical position accumulators 108 and 110 track the horizontal and vertical positions X and Y of the image beam, respectively, according to the following equations: (26) X_n= X_n-1+ a_j2π / M (27) Y_n= Y_n-1 + c_i(n_v/ n_h) 2π / M Here a_jRepresents a linear approximation of the horizontal sweep function X (t) at 2π / M, c_iIs (n_v/ n_h) Represents a linear approximation of the vertical sweep function Y (t) at 2π / M. For example, if X (t) and Y (t) are sine waves according to the above equations (1) and (2), there are effectively many sine waves (_j,_i) Can be expressed as before by the expansion of each Taylor series, which is decomposed into line segments. The more line segments used, the more accurate the linear approximation. A_jAnd c_iIs the slope of these line segments in units of distance per radian (with respect to the source pixel), where the j = 0 to jth line segments are approximations of X (t), i = 0 to ith. The line segment of is an approximation of Y (t). Therefore, a_j2π / M is the horizontal distance in pixel ph that the beam moves in one clock "step", c_i(n_v/ n_h) 2π / M is the pixel p that the beam moved in one clock "step"_vIs the vertical distance in. The horizontal and vertical position accumulators 108 and 110 have horizontal and vertical phase θ._nAnd Ψ_nBased on memory 112 to a_jAnd c_iTake out each, θ_nAnd Ψ_nThe accumulators 108 and 110 retrieve the updated values by a_jAnd c_iTaken out until you update a_jAnd c_iTo store.

Further referring to FIGS. 15 and 16, an example showing the steps of the horizontal position accumulator 108 according to the embodiment of the present invention is presented. FIG. 16 is a plot of the horizontal and vertical sweep sine waves X (t) and Y (t) of FIG. 5A and their respective linear approximations when j = i = 0,1. That is, X (t) is the inclination a₀= (8 pixels) / (π radians) and a₁The approximation is defined by two line segments j = 0 and j = 1 with =-(8 pixels) / (π radians), respectively. Therefore, the horizontal position accumulator 108 has -π / 2 &lt;θ._nIn + π / 2, a in equation (26)₀Using, + π / 2 &lt;θ_nIn -π / 2, a in Eq. (26)₁To use. Specifically, θ_nWhen is transitioning from less than or equal to -π / 2 to above -π / 2, the horizontal position accumulator 108 is in memory 112 to a.₀Take out, θ_nTo be used repeatedly until is greater than + π / 2 a₀To store. θ_nWhen is greater than + π / 2, the accumulator 108 is in memory 112 to a₁Take out, θ_nTo be used repeatedly until is greater than -π / 2 again a₁To store. As a result, the accumulator 108 only needs to access memory 112 twice per horizontal sweep cycle.

Using the above example, the vertical position accumulator 110 operates in a similar fashion. Y (t) is the slope c₀= (6 pixels) / (π radians) and c₁The approximation is defined by two line segments i = 0 and i = 1, which have =-(6 pixels) / (π radians), respectively. The accumulator 110 has -π / 2 &lt;Ψ_nIn + π / 2, c in Eq. (27)₀Using, + π / 2 &lt;Ψ_nFor -π / 2, c in Eq. (27)₁To use. Specifically, Ψ_nWhen transitions from less than or equal to -π / 2 to above -π / 2, the vertical position accumulator 110 is in memory 112 to c.₀Take out, Ψ_nC for repeated use until is greater than + π / 2₀To store. Ψ_nWhen becomes greater than + π / 2, the accumulator 110 retrieves c1 from memory 112 and Ψ_nStore c1 for repeated use until is greater than -π / 2 again. As a result, the accumulator 110 only needs to access memory 112 twice per horizontal sweep cycle.

With reference to FIG. 15 again, the horizontal and vertical position transducers 114 and 116 shift the horizontal and vertical positions X and Y according to the following equation to fit the grid pattern 42 (FIG. 13). (28) X_translated= X_n+ ph / 2-0.5 + L_h (29) Y_translated= Y_n+ P_v/2-0.5+L_v Here L_hAnd L_vIs an optional matching correction factor, as explained below.

Specifically, X_nAnd Y_nDoes not fit grid pattern 42 (FIG. 13) because it relates to the amplitude of the sweep functions X (t) and Y (t) in pixels. For example, p as shown in Fig. 13._h= 8 and P_vIf = 6, and X (t) and Y (t) are sine waves, then X is due to the amplitude of the horizontal and vertical sweep sine waves (Figure 16)._nIs in the range of -4 to +4 pixels, Y_nIs in the range of -3 to 3 pixels.

To fit grid pattern 42 (Figure 13), X_translatedIs in the range of -0.5 to +7.5, and Y_translatedIs preferably in the range of -0.5 to +5.5. Therefore, equations (28) and (29) are X._nP_hEffectively shifts by /2-0.5=3.5 pixels, Y_nP_vBy effectively shifting by / 2-0.5 = 2.5 pixels, these Xs_translatedAnd Y_translatedTo obtain each suitable range of.

L of equations (28) and (29)_hAnd L_vMathematically reveal the image beam inconsistency, respectively. In one embodiment of the invention, the horizontal and vertical phase accumulators 104 and 106 are θ as the reflector (FIG. 17) rotates through the horizontal 0π position._n= 0 and Ψ when the reflector rotates through the vertical 0π position_nEach is calibrated to = 0-reflector positions are measured using conventional techniques as described in US Pat. No. 5,648,618 to Neukermans, "Micromachine Hinge with Integrated Twist Sensor". , This shall be incorporated by reference. However, if the image beam does not collide with the respective horizontal or vertical center of the display screen (Figure 1) as the reflector rotates through the horizontal and vertical 0π positions, the actual position of the beam will be from the position indicated by the reflector position. It is offset. Since this offset is usually measurable and often substantially constant regardless of beam position, the x and y components of the offset are represented by constants Lh and Lv with pixel units, respectively. .. That is, L_hAnd L_vBy including in equations (28) and (29), X_translatedAnd Y_translatedRepresents the actual position of the beam, not just the position of the reflector. This technique is particularly useful when the image generator (Figure 17) scans a color image by sweeping three inconsistent beams, the red (R), green (G), and blue (B) beams. .. Separate X for each beam_translatedAnd Y_translatedBy calculating the value of, the image generator is L_hred, L_vred, L_hgreen, L_vgreen, L_hblue, And L_vblueThis inconsistency can be mathematically corrected during interpolation of scan pixel Z (Figure 13) using the appropriate value of.

In one embodiment of the invention, the horizontal and vertical position transducers 114 and 116 are X._translatedAnd Y_translatedIt is a floating point counter in which the integer part of is the coordinate of the lowest numbered pixel P and the decimal part is β and α, respectively. For example, see FIG. 14, scan pixel Z_{x + β, y + α}If the image beam is placed to form an X_translatedAnd Y_translatedThe integer part of is equal to x and y, respectively, and the fractional part is equal to β and α, respectively.

Further referring to FIG. 15, the interpolator 118 is X in the conventional form as described above in connection with FIG._translated= x + β and Y_translatedInterpolate the intensity of scan pixel Z from the value of = y + α.

Other embodiments of the position tracking and interpolation circuit 100 are also conceivable. For example, scan pattern 40 (FIG. 13) appears repeatedly, and the period of the pixel clock, and thus the position of pixel Z, is known in advance, so X_translatedAnd Y_translatedAll possible values for can be pre-determined and stored in a look-up table (not shown). Therefore, the interpolator 118 is X from this look-up table._translatedAnd Y_translatedAll you have to do is take out. However, such circuits include two memory accesses per pixel clock cycle. This is one line segment j and i, and therefore one more slope a_jAnd c_iIt differs from circuit 100 in FIG. 15, where horizontal and vertical position accumulators 108 and 110 access memory 12 only when changing from one to another. In addition, if the non-linear horizontal pixel clock is used in FIG. 13 so that the pixel Z aligns with the vertical line of the grid 42, i.e. β is always zero, the circuit 100 is in vertical position y + α. Only may be calculated. In these embodiments, the horizontal converter 114, along with the interpolator 118, can be replaced by a counter clocked by a non-linear horizontal pixel clock, while circuits 106, 110, and 116 are linear produced by circuit 102. Clocked by the pixel clock. Image generator

FIG. 17 is a block diagram of an image generator 130 that can carry out the above method according to an embodiment of the present invention. The image generator 130 includes a scanning assembly 132, an image beam generator 134 that produces an image beam 136, and a source image buffer 138.

The scanning assembly 132 includes a sweep drive circuit 140 and a conventional reflector 142 such as the reflector 22 of FIG. Circuit 140 drives reflector 142 so that the reflector sweeps the beam in a double sine wave and / or bidirectionally in the vertical dimension, as described above in connection with FIGS. 4, 5A, 5B, and 12. it can.

The image beam generator 134 includes a position intensity circuit 144, a scanning pixel interpolator 146, a conventional beam source 148, and a buffer switching circuit 150. Circuit 144 can modulate the intensity of beam 136 according to the position of the beam, as described above in connection with FIGS. 11 and 12. Interpolator 146 can modulate the intensity of beam 136 to interpolate the intensity of scan pixel Z, as described above in connection with FIGS. 13 and 16, and may include circuit 100 of FIG. The beam source 148 may generate a beam 136, for example, a light emitting diode (LED) or a laser diode. The switching circuit 150 separates the generation of the image beam 136, and thus the formation of the scan pixel Z, from one source image in the buffer 138, as described above in connection with FIGS. 9 and 10. Transition to the source image of, and reduce or eliminate the vicinity of the fake ghost image.

The source image buffer 138 is a conventional buffer that receives a source video or still image in a conventional manner from a conventional source. For example, buffer 138 may receive video images via a stream of video data from a computer (not shown) or the Internet (not shown).

Further referring to FIG. 17, other embodiments of the image generator 130 are conceivable. For example, the beam 136 may be an electron beam for display on a fluorescent screen of a cathode ray tube (CRT), and the reflector may be a coil or other device for sweeping the beam. When the beam 136 is a light beam, the reflector may direct the light beam to the display screen (FIG. 1) or directly to the viewer's eye (not shown). Further, in the above, "horizontal" and "vertical" are used to indicate the left-right and top-bottom dimensions that are orthogonal to each other, but may indicate other dimensions that may not be orthogonal to each other. For example, "vertical" may generally indicate a dimension having a low sweep frequency, even if it is not in the upper and lower dimensions.

The above description is presented so that those skilled in the art can create and use the present invention. Various modifications to the embodiments will be readily apparent to those skilled in the art, and the general principles of the present specification may be applied to other embodiments and applications without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the illustrated embodiments, and the present invention is given a maximum range consistent with the principles and features disclosed herein.

<figref num="1">Diagram showing a conventional optical image display system</figref><figref num="2">The figure which shows the plot of the sine wave which shows the position of the image beam of FIG. 1 in the horizontal dimension in contrast with time.</figref><figref num="3">The figure which shows the plot of the sawtooth wave which shows the position of the image beam of FIG. 1 in the vertical dimension in contrast with time.</figref><figref num="4">The figure which shows the plot of the double sinusoidal image scanning pattern superimposed on the source image grid pattern by embodiment of this invention.</figref><figref num="5A">FIG. 5 shows plots of horizontal and vertical sweep sine waves relative to time, according to an embodiment of the invention, where the sine waves have a suitable phase relationship to generate the scanning pattern of FIG.</figref><figref num="5B">FIG. 5 shows plots of horizontal and vertical sweep sine waves relative to time, according to an embodiment of the invention, where the sine waves also have another suitable phase relationship that produces the scanning pattern of FIG.</figref><figref num="6">The figure which shows the plot of the double sine wave scanning pattern of FIG. 4 when the phase relationship between the horizontal and vertical sweep sine waves according to the embodiment of this invention is not optimal.</figref><figref num="7">The figure which shows the plot of the double sinusoidal scanning pattern of FIG. 4 when the phase relation between the horizontal and vertical sweep functions by embodiment of this invention is the worst case.</figref><figref num="8">FIG. 5 shows plots of horizontal and vertical sweep functions relative to time, according to an embodiment of the invention, where the sine wave has the worst-case phase relationship that produces the scan pattern of FIG.</figref><figref num="9">A diagram showing a sequence of double sinusoidally scanned video images in a way that makes the viewer perceive a fake ghost object.</figref><figref num="10">A diagram showing a sequence of double sinusoidally scanned video images in a manner that reduces or eliminates the viewer's perception of false ghost objects according to an embodiment of the invention.</figref><figref num="11">A diagram showing a plot of a double sinusoidal scan pattern that can result in non-uniform brightness in the resulting scanned image.</figref><figref num="12">The figure which shows the plot of the horizontal and vertical sweep functions as compared with time when the vertical sweep function was modified according to embodiment of this invention to improve the brightness non-uniformity of the resulting scanned image.</figref><figref num="13">FIG. 4 shows a plot of the scan and grid pattern of FIG. 4 according to an embodiment of the present invention, and illustrates a method of interpolating pixels of a scan image from pixels of a corresponding source image.</figref><figref num="14">A diagram illustrating a part of the scanning and grid pattern of FIG. 13 according to an embodiment of the present invention and exemplifying a method of interpolating pixels of a scanning image from pixels of a corresponding source image.</figref><figref num="15">A block diagram of an interpolation circuit according to an embodiment of the present invention that can interpolate pixels in a scanned image using the techniques illustrated in FIGS. 13 and 14.</figref><figref num="16">A diagram showing a plot of the horizontal and vertical sweep sine waves of FIG. 5A and a line segment used by the interpolation circuit of FIG. 15 to obtain a linear approximation of the sweep sine wave according to an embodiment of the present invention.</figref><figref num="17">Block diagram of an image generator according to an embodiment of the invention that can function as described above in connection with FIGS. 4-16.</figref>