Mtf-improved optical system employing phase mask with unchanged phase in central region

The present invention relates to improved wave surface coding optics for controlling focus-related aberrations and methods of designing such wave surface coding optics.

Wave surface coding is a relatively new technology that uses a wave surface coding optics that operates by adding an aspheric phase change to the wave surface of the light entering from the subject being imaged, resulting in misfocusing of the sampled imaging system. Used to reduce the impact. Image processing of the resulting image is required to eliminate the spatial effects of wave surface coding. The processed image is crisp and clear, while at the same time being relatively unaffected by the distance between the subject and the detector. Wave surface coding is also used to control common focus-related aberrations, thereby allowing a simplified design of the imaging system while providing alias removal for the sampled imaging system.

The wave surface coding optics taught and described in the prior art beginning with US Pat. No. 5,748,371 issued May 5, 1998 were discovered by trial and error. The first valid wave surface coding mask applied a cubic phase function to the wave surface entering from the subject. It has been known that wave surface coding optics such as cubic masks need to apply asymmetric phase changes to the wave surface.

Prior art related to wave surface coding systems includes a basic description of wave surface coding (US Pat. No. 5,748,371) and a description of wave surface coding used for alias removal (alias removal devices and methods for optical imaging). , U.S. Pat. No. 6,021,005, February 1, 2000), Usage of Wave Surface Coding in Projection Systems (Devices and Methods for Extending the Depth of Field in Image Projection Systems, U.S. Pat. No. 6,069,738 (May 30, 2000), and a combination of wave surface coding and amplitude apodizer (devices and methods for reducing imaging errors in imaging systems with extended subject depth, U.S. Pat. No. 6,097,856). The specification, August 1, 2000) is included.

The layout of a conventional wave-coded imaging system is shown in Figure 1. The imaging optics 104 collects light reflected or transmitted from the subject 102. The wave surface coding optics 106 changes the phase of the light in front of the detector 108. The wave surface optical system 106 includes a cubic mask. The detector 108 may be an analog film, CCD or CMOS detector, or the like. The image obtained from the detector 108 is spatially blurred due to the wave surface coding optics 106. Image processing 110 is used to remove spatial blur and result in a final image. That is, the image processing 110 removes the wave surface coding applied by the optical system 106, thereby undoing the effects of the optical system 106 except for the increase in depth of field and depth of focus. Images before and after image processing 110 are also extremely insensitive to misfocus aberrations (very). insensitive). These misfocus aberrations occur when the subject 102 exceeds the depth of field of the imaging optics 104, the detector 108 exceeds the focal depth of the imaging optics 104, or spherical aberration, chromatic aberration, petzval curvature, astigmatism. It may result from the imaging optics 104 having several combinations of misfocus aberrations such as aberrations, temperature or pressure related misfocus.

Figure 2 illustrates the phase function of prior art prior art wave-plane coding that is separable in the perpendicular direction, which creates an extended depth of field. This phase function is a simple cubic phase function and is mathematically described as follows with standardized coordinates.<maths num="1"><img file="JP4975239B2_D0001.tif" /></maths>Other relational expressions of the cubic mask are described as follows: Third-order relation (x, y) = a [sign (x) | x |^b+ sign (y) | y |^b] here<maths num="2"><img file="JP4975239B2_D0002.tif" /></maths>And<maths num="3"><img file="JP4975239B2_D0003.tif" /></maths>Is. These relational expressions follow a "tertiary" profile with an increasing gradient near the end of the opening.

The upper plot in Figure 2 describes a 1D slice along the orthogonal axis of the cubic phase function. The lower plot in Figure 2 describes the constant phase contours of this cubic phase function.

Figure 3 shows the MTF as a misfocus function for systems without wave-plane coding and systems with the conventional wave-plane coding cubic phase function of Figure 2. The normalized misfocus value is the same for both systems and is given by Ψ = {0,2,4}, where Ψ = [2πW₂₀] And here W₂₀Is the coefficient of conventional misfocus aberration in the wave. MTF (302) without wave surface coding appears to change significantly with misfocus. MTF (304) with a orthogonally separable cubic phase function appears to be far more misfocused than systems without wave-plane coding.

The inseparable prior art formula for wave-plane coding optics is in standardized coordinates.<maths num="4"><img file="JP4975239B2_D0004.tif" /></maths>Is. This phase function has been shown to be useful in controlling misfocus and minimizing optical power or alias removal at high spatial frequencies. When using a digital detector such as a CCD or CMOS device to capture image 108, optical power that exceeds the detector's spatial frequency limit results in disguise or "alias" as low spatial frequency. For example, it can be said that the standardized spatial frequency limit of a digital detector is 0.5. As can be seen from FIG. 3, a focused MTF derived from a conventional system without wave surface coding can generate a large amount of optical power beyond this spatial frequency limit, which can cause aliases. By adding misfocus to systems that do not have wave surface coding, as is well known, the total optical power of high spatial frequencies can be reduced and aliasing is reduced. As shown in FIG. 3, conventional wave surface coding can be used to reduce the total optical power that can cause aliases compared to systems without wave surface coding (302) (304).

The image processing function 110 basically applies amplification and correction of phase as a function of spatial frequency, thereby making the unprocessed MTF a focused MTF derived from a conventional system without wave surface coding. Restore after processing, or restore to some other application-specific MTF if necessary. In essence, the image processing function of FIG. 1 removes the blurring of the wave surface coding in the detected image.

In practice, the amplification applied by the image processing function not only increases the power of the deterministic image, but also the additional random noise power as well. When image processing 110 is implemented as a linear digital filter, the additional increase in random noise power is called the noise gain of the digital filter. The concept of "noise gain" is commonly used in radar systems to describe the total noise power at the output of a radar digital processor. A non-linear implementation of image processing 110 has a similar type of noise-related measurement. The noise gain for a digital filter is defined as the ratio of the RMS value of the filtered noise to the root mean square (RMS) value of the unfiltered noise. In general, the noise gain is almost always greater than the noise gain of a wave-coded system. Assuming that the additional noise does not correlate with white Gaussian noise, the noise gain of a two-dimensional linear digital filter can be shown to be equal to:<maths num="5"><img file="JP4975239B2_D0005.tif" /></maths>here<maths num="6"><img file="JP4975239B2_D0006.tif" /></maths>And f (i, k) is a spatial domain digital filter, F (w)_i, w_k) Is an equivalent frequency domain digital filter, the first sum is the sum over the indicators i or k, and the second sum is the sum over the other indicators. The index (i, k) indicates the spatial area coordinates, whereas the index (w)_i, w_k) Indicates frequency domain coordinates. The constraint that all the filter values and the sum of the zero spatial frequency filter values are both equal to the unity ensures that the zero spatial frequency component of the image (eg, the background) cannot be changed by image processing. ..

The wave-coded MTF with the highest value requires minimal amplification by a digital filter and therefore has minimal noise gain. In practice, a wave-plane coding optic that produces MTFs with small changes over the desired amount of misfocus and also has the best MTF is considered to be the best and most practical optics for wave-plane coding. Optics that produce not only MTFs with small changes due to misfocus but also extremely low MTFs are impractical due to the extremely large noise gain of the resulting digital filter. Digital filters with high noise gain will produce a final image with unnecessarily high levels of noise.

Conventional cubic wave surface coding masks work to increase depth of field and control focus-related aberrations, whereas the technology retains the ability to reduce focus-related aberrations while maintaining high MTF values. There remains the need for improved wave surface coding optics that also occur. The need for a method of designing such an improved wave surface coding optic remains in the art.

<p> An object of the present invention is to provide an improved wave surface coding optical system that retains the ability to reduce focus-related aberrations while also producing high MTF values, and to design such an improved wave surface coding optical system. To provide a method.</p>

<p> The improved wave-plane coding optics according to the invention, which impart a phase profile to the wave-plane of light entering from the imaged subject, increase the resulting MTF while leaving it less susceptible to focus-related aberrations. Let me. Such improved wave-plane coding optics have a phase region in which the central part of the given phase profile is essentially constant, while the edges of the phase profile alternate between negative and positive (eg, each profile). It has the property of having (upward and downward) at the ends.</p><p> In order to achieve higher MTF, control misfocus and misfocus aberrations, and improve alias removal characteristics, the center group of light rays needs to be left unaltered by the wave-plane coding optics. The outer rays need to be altered in order to increase the focusing (possibly spatial resolution) of the system with a fully open aperture. Only these outer rays need to be modified to increase the focus while keeping the depth of field and / or aliasing characteristics constant.</p>

There are a myriad of wave-plane coding optics that will reduce the changes in MTF and PSF of a given optic that result from misfocus or misfocus aberrations. Many of the possible optics are used to remove the blurring due to wave surface coding from the detected image, above the level at which the required image processing function 110 can accept the additional noise in the actual image. It is impractical because it amplifies. Improved wave-plane coding optics that can control misfocus and misfocus aberrations, lead to higher MTFs, and have improved aliasing characteristics, as well as new methods of wave-plane coding design. Is shown in Figures 5-9. The usage of these improved wave surface coding optics and the design method for controlling misfocus aberrations with Cooke triple lenses are shown in Figures 9-11.

The improved wave surface coding optical system according to the present invention shares the characteristic that the central region of the given phase profile is basically constant, while the edges of the phase profile have a phase region of alternating negative and positive. To do. Not only do such wave-plane coding optics retain the potential to reduce focus-related aberrations, but they also have a significantly higher MTF than traditional wave-plane coding optics, resulting in reduced noise in the final image produced. ..

To reorient the rays as a function of spatial position, wave-plane coding optics (in the form of aspherical optics) are installed at or near the aperture diaphragm of the optical system (or images of the aperture diaphragm or near it). .. The aspherical optics can be made of optical glass or plastic with varying thickness and / or refractive index. The optics can also be mounted with molded mirrors, spatial light modulators, holograms, or micromirror devices. U.S. Pat. No. 6,021,005, entitled "Alias Removal Devices and Methods for Optical Imaging," issued February 1, 2000, provides a variety of variations for the wave front of light entering from a subject. Provides a description of the device.

The light beam from an ideal thin lens that does not have wave surface coding and focuses from the lens to a focal point of 50 mm is shown in the upper graph of Figure 4. All rays from an ideal system without wave surface coding propagate towards the best focal position on the optic axis. Rays from a conventional (prior art) perpendicularly separable cubic phase system are shown in the lower graph of FIG. It should be noted that the light rays coming from the upper half of this lens cross the optic axis beyond the best focal position (or 50 mm) of a conventional lens. Light rays originating from the lower half of this lens intersect the optic axis just before the best focal position of a conventional lens.

All rays in a cubic phase system of prior art wave surface coding are compared to systems without wave surface coding, as two rays from the prior art wave surface coding system do not intersect the optic axis at the same point. Then it is changed (except for the zero-gradient ray on the axis). In order to achieve higher MTF, control misfocus and misfocus aberrations, and improve alias removal characteristics, the group of light center centers should remain unchanged.

Consider an optical system that does not use conventional wave surface coding in the fully open aperture and throttled state. It is assumed that a particular application has a depth of field (or depth of focus) and / or alias removal requirement that a fully open aperture system cannot meet. It is well known that squeezing the lens increases the depth of field of the system while reducing the possible spatial resolution of the optical system. Narrowing the aperture also reduces the optical power available to the detector. There is a specific aperture stop where the imaging system has the best fit for the required depth of field and / or alias removal characteristics. At that time, the light beam passing through the aperture of the narrowed system is considered appropriate for a particular application in terms of depth of field and / or alias removal.

In order to increase the focusing (possibly spatial resolution) of the fully open aperture system, the rays of the fully open aperture system that are outside the narrowed aperture need to be modified. Only those rays outside the narrowed aperture need to be modified in order to increase the focus while keeping the depth of field and / or alias removal characteristics constant. The resulting MTF is not as high as possible and the resulting noise gain is possible when the rays in the focused aperture are modified, as in all prior art wave surface coding optics. Not as low as possible, the resulting image has more noise than necessary.

By not modifying the central ray group of the wave surface coding system, the resulting MTF below the spatial frequency of the digital detector can be enhanced above the prior art wave surface coding system. Only the rays outside the central region of the aperture need to be modified to control misfocus or misfocus aberrations. The central region is defined as the overall region of the narrowed aperture, and despite reduced focus and spatial resolution, the system has a depth of field, depth of focus, or alias that is appropriate for a particular application. Will have removal properties.

The improved perpendicularly separable wave surface coding optics can be described most generally through phase functions, which in standardized coordinates<maths num="7"><img file="JP4975239B2_D0007.tif" /></maths>Has the shape of, here<maths num="8"><img file="JP4975239B2_D0008.tif" /></maths>And here<maths num="9"><img file="JP4975239B2_D0009.tif" /></maths>Is. The total is the total over the index i. Function U (| x | / A_x) Is a step function of 0/1 and has a length of 2A_xIt has a value of zero inside the opening and a value of 1 outside this opening. Function G_xAnd G_yIs a general function and A_xAnd A_yMake changes to the rays of the system outside the specific aperture defined by. The openings formed in this form are described in rectangles for mathematical convenience, but can be described in any closed shape. For example, circular, elliptical, or multi-sided polygonal openings can be used instead of rectangular openings.

In order for the phase function to control the misfocus effect, the phase function G_xAnd G_yHowever, it must be designed so that a group of rays originating from a particular region of the aperture intersects the optic axis either before or after the point of best focus when no wave surface coding is used.

With these concepts, it is possible to form several improved perpendicularly separable wave surface coding optics. These optics are the general function G_xAnd G_yIt depends on the configuration of. For example, an optical system in the primary phase region<maths num="10"><img file="JP4975239B2_D0010.tif" /></maths>Can be described here<maths num="11"><img file="JP4975239B2_D0011.tif" /></maths>Is. The system of the linear phase region is A_xAnd A_yIt has a zero phase inside the aperture defined by, and outside this aperture linearly changes the phase as a function of the spatial position variables x and y. The system in the primary phase region provides an extended depth of field and has a high MTF below the spatial frequency limit of the digital detector. This system also has a very simple physical shape, which may be recommended over smoothly changing shapes due to the manufacturing process or physical mounting used.

For example, if the wave surface coding optics are machined on a precision mill, optics in the primary phase region would be recommended over cubic phase optics, for the reason. This is because the optical system in the phase region has only a constant surface inclination, whereas the cubic phase optical system has a surface inclination that continuously changes. Often, an optical element with a constant surface inclination is easier to process than an element with a continuously changing inclination. If the wave-plane coding optics are mounted with micromirrors, etc., it is easier to mount a small number of surface tilts of the system in the primary phase region than the continuously changing surface tilts of the prior art tertiary phase optics. May be done.

Another version of the improved perpendicularly separable wave surface coding optics is mathematically explained by the sum of the phase functions in the power sum region. This phase function<maths num="12"><img file="JP4975239B2_D0012.tif" /></maths>Is defined as, here<maths num="13"><img file="JP4975239B2_D0013.tif" /></maths>And the total is the total over the index i.

Examples of linear phase region systems and power sum region systems are found in Figures 5, 6 and 7. The graph in Figure 5A shows the ray path out of one range of the system in the linear phase region. The graph in Figure 5B shows the ray path for one range of the system of cubic phase regions. The system of the phase region of the cubic equation is the system of the power sum region with only a single term, the power of this term has a number of 3, or β for i 1._i= δ_i= 3, and α_i= χ_i= 0.

From FIG. 5A, it can be seen that the light rays originating from the central region of the lens (which extends from -2.5 to +2.5 mm) have not been altered by the system of the linear phase region. All unaltered rays propagate toward the optic axis at the best focal position of 50 mm on the right side of the lens. Only the outer rays greater than +/- 2.5 mm from the lens are subject to modification by the linear phase region function. Light rays coming from the top of the lens are modified to intersect the optic axis at points beyond the best focal position. Rays coming from the bottom of the lens intersect the optic axis at a point just before the best focal point.

From FIG. 5B, the system of the cubic phase region is also unchanged in the central region of the lens (from -2.5 mm to +2.5 mm). The remaining rays intersect the optic axis at a point where one set of rays (derived from the top of the lens) is ahead of the best focal position, and the other set of rays (derived from the bottom of the lens) has the best focus. Changes can be made in a spatially variable manner so that they intersect the optic axis at a point in front of the position.

A system of linear phase regions and a system of exponentiated phase regions can consist of different regions with different slopes and / or different numbers of terms. For example, a system of linear phase regions as shown in FIG. 5A has two regions that change linearly with the central region of zero phase, instead of having two regions that change linearly with the central region of zero phase. It is possible to have an area that exceeds. Additional regions may direct light to different locations for better control of misfocus, misfocus aberrations, and alias removal characteristics. The size and shape of the misfocused PSF can also be visualized and controlled by controlling the region of the phase function and the corresponding rays. Manual optimization is possible when only two asymmetric regions of the phase function are used (as in Figure 5A). When the number of regions exceeds 2, the number, size, and phase of each region are generally best determined by computer optimization.

FIG. 6 gives another view of the wave surface coding system for the linear phase region and the cubic phase region. The graph at the top of Figure 6 shows a 1D slice of the phase function that describes the optics of both systems along one of the orthogonal axes. The system of this linear phase region in 1D format is<maths num="14"><img file="JP4975239B2_D0014.tif" /></maths>Is. Especially 1D for the system of the phase region of the cubic equation<maths num="15"><img file="JP4975239B2_D0015.tif" /></maths>Is. Steady-state 2D contours for these phase functions are shown at the bottom of FIG. These contour lines clearly show that the phase within the central region of these systems is constant, i.e. the rays at the center of the corresponding wave surface coding system are unaltered. The phase near the edge of the system in the linear phase region increases / decreases linearly, while the phase near the edge of the system in the cubic phase region increases / decreases as a cubic function.

Figure 7 shows the misfocus MTF as a function of normalization for systems without wave surface coding, systems in the linear phase region, and systems in the tertiary phase region. The normalized misfocus value is Ψ = {0,2,4} as used in Figure 3. MTFs derived from both linear and cubic phase region systems are very close to each other (as a result, not particularly distinguished in Figure 7) and are extremely misfocused, especially when compared to systems that do not use wave surface coding. Less susceptible. The heights of the improved wave surface coded MTFs in FIG. 7 are compared with those of the prior art cubic phase coded MTFs shown in FIG. MTFs derived from both linear and cubic phase region systems are higher than traditional cubic phase wave surface coded MTFs, while all wave surface coding MTFs are essentially for misfocus. Less susceptible. From the point of view of alias removal, the MTF derived from the improved first-order phase region and third-order phase region system is usually higher in low spatial frequency without aliasing than the prior art third-order phase MTF. It also lowers the optical power at high spatial frequencies compared to systems that have a value MTF, while not having wave-plane coding.

An improved inseparable wave surface coding optic can also be described. Common inseparable wave surface coding optics<maths num="16"><img file="JP4975239B2_D0016.tif" /></maths>It is possible to be mathematically defined through the form of, here<maths num="17"><img file="JP4975239B2_D0017.tif" /></maths>And the total is the total over the index i. Function Q (p / Ω__i) Is a 0/1 function that allows the central ray group derived from a region with a radius smaller than Ω_ to remain unchanged. Function G_i(p, θ) is a general phase function, positive and negative so that the region of the ray intersects the optic axis either before or before the best focal image point. It has a phase region.

One common example of an improved inseparable wave surface coding optic is mathematically<maths num="18"><img file="JP4975239B2_D0018.tif" /></maths>Explained as, here<maths num="19"><img file="JP4975239B2_D0019.tif" /></maths>Is. Another paradigm for improved inseparable wave surface coding optics<maths num="20"><img file="JP4975239B2_D0020.tif" /></maths>Is an inseparable exponentiation form given by<maths num="21"><img file="JP4975239B2_D0021.tif" /></maths>The integer M controls the number of +/- sectors used, and the sum is the sum over the variable i.

An example of an improved inseparable power sum of wave plane coded optics is given in Figure 8. The upper left graph in FIG. 8 is a contour plot of the stationary phase of the inseparable cubic phase sector system. This cubic phase sector system is an inseparable power sum system with one power term and β = 3. Offset = π / 2 at M = 1. This inseparable cubic phase sector system is<maths num="22"><img file="JP4975239B2_D0022.tif" /></maths>And here<maths num="23"><img file="JP4975239B2_D0023.tif" /></maths>Is. The graph in the upper right of FIG. 8 shows a 1D slice passing through a system of cubic phase sectors. The graph at the bottom of FIG. 8 shows the misfocused MTF of a system without wave surface coding and a system with an inseparable cubic phase sector system. Again, the standardized misfocus value is Ψ = {0,2,4} as used in Figures 3 and 7. These MTFs are 1D slices derived from MTFs formed with circular openings. MTFs for systems with inseparable cubic phase sector systems appear to be extremely less susceptible to misfocus effects, especially when compared to MTFs derived from systems without wave surface coding.

Figures 9, 10 and 11 illustrate one example of how to use improved wave surface coding optics to control misfocus aberrations. This paradigm shows the control of field-dependent aberrations by a normal Cooke triple lens used in visible light. See Modern Optical Engineering (Warren J. Smith, McGraw-Hill, Inc, NY, 1990) for more information on Cooke triplets. A drawing of this lens is given in FIG. The resulting noise gain from the improved wave surface coding optics when compared to the prior art wave surface coding optics is shown to be factorized 2.5 smaller than the system with this lens. This reduced noise gain directly transforms into a final image with 2.5 times less noise than the prior art system.

This triplet uses a spherical surface, except for the second surface of the second or intermediate lens, which includes the wave-plane coding optics. The rules for triple lenses that do not have wave surface coding<tables num="1"><img file="JP4975239B2_D0024.tif" /></tables>Given by. All dimensions are given in mm. The focal length of this lens is 50mm, the full aperture F / # is 5, and the half field of view is 20 degrees. This lens is used in a system with a digital gradation detector. The pixel pitch is 7.6 microns for a square pixel with a 100% fill ratio. The spatial frequency limit of this detector is 65.8 lp / mm. The ambient temperature is considered to be fixed at 20 degrees C at a pressure of 1 atm. Ideal manufacturing and assembly are also envisioned.

Although the lens of FIG. 9 is a properly complex multi-glass optical system, this system suffers from monochromatic misfocus aberrations of spherical aberration, petzval curvature, and astigmatism, which limit off-axis performance. If the lens is designed with a single optical material instead of the two different materials actually used, the lens will also suffer from increased chromatic aberration. If plastic optics were used instead of glass optics, the lens would also suffer from temperature-related misfocus effects.

Figure 10A (prior art) shows the performance of the system of Figure 9 operating at (widely open) F / 5, and Figure 10B shows the system of Figure 9 with the aperture throttled to F / 19. .. Each of the graphs following them relates to the measurement of the lens with green light. A contour plot of the optical path length (OPD) of the exit pupil on the axis for the F / 5 system is given on the left of Figure 10A. The peak-to-valley OPD for this exit pupil has a value of about 0.7λ. The plot on the right in Figure 10A describes the MTF of the F / 5 system as a field angle function with respect to the axes, 14 degrees, and 20 degrees. All included in these MTFs, and following the MTFs, are pixel MTFs for 7.6 micron square pixels with a 100% fill ratio. Only 1D slices along the horizontal axis of the 2D diffraction-limited MTF and the 2D wave-coded MTF are shown in Figures 10 and 11. The MTF, which is a function of the angle of view, seems to change significantly in the conventional F / 5 system due to the presence of aberrations.

The effect of narrowing the lens from F / 5 to F / 19 can be seen in the graph in Fig. 10B. The OPD from the peak to the valley of the narrowed exit pupil on the axis is lowered to 0.12λ. The MTF, which is a function of the angle of view of the narrowed system, seems to be almost unchanged compared to the full-aperture system. Narrowing the aperture is one way to control the aberrations of this system, but (5/19)²A reduction factor of or 93% loss of optical power is captured by the full aperture system.

Figures 11A and 11B show the performance of the Cooke triplet of Figure 9 modified to utilize wave surface coding. The wave-plane coding optics for this paradigm were modeled as being added to the aperture diaphragm of the system on the second surface or surface # 4 of the second element. The prior art wave surface coding cubic phase equation used in Figure 11A for the phase system is<maths num="24"><img file="JP4975239B2_D0025.tif" /></maths>And here the surface height Z_{prior art}(x, y) is given in mm. The optical area used is a circle with a radius of 3.86 mm. In practice square openings can also be used.

The improved wave surface coding cubic phase region system used in Figure 11B shows the surface equations.<maths num="25"><img file="JP4975239B2_D0026.tif" /></maths>And here again the surface height Z_improved(x, y) is given in mm, the optical area used is a circle with a radius of 3.86 mm, and in practice a square aperture can also be used.

The graph in Figure 11A illustrates the use of prior art's perpendicularly separable wave plane coding cubic phase optics. The graph in Figure 11B illustrates the use of an improved perpendicularly separable cubic phase region wave plane coding optic. The use of improved wave surface coding optics increases the height of the MTF prior to image processing 110 and is therefore required to provide ideal post-processing performance when compared to prior art optics. Drastically reduce the noise gain of the filter. The improved MTF also has higher optical power below the detector spatial frequency cutoff and is accompanied by a significantly reduced MTF above the detector cutoff when compared to traditional full aperture systems. It also shows the alias removal performance increased by.

The prior art cubic phase system was designed to have peak-to-valley OPDs above approximately 9.5λ of the wide open (F / 5) exit pupil on the axis. Prior to image processing, the resulting MTF as a function of the angle of view is basically as shown in Figure 11A, especially compared to the full-open F / 5 system in Figure 10A without wave-plane coding. It is constant. The diffraction limit MTF for this system is selected as the desired system performance of the wave surface coding system after image processing 110. In general, the resulting PSF and MTF in the wave surface coding system after image processing can have almost any form. In this example, the image processing function 110 converts the pre-image processing wave surface coding MTF into a processed MTF that closely matches the ideal diffraction-limited MTF with a detector spatial frequency cutoff of 65 lp / mm or less. 2D linear filter is implemented. The resulting digital filter noise gain value is then used as a figure of merit to determine the two-dimensional MTF height compared to the desired diffraction-limited MTF. For the prior art third-order phase system in Figure 11A, the resulting 2D digital filter has a noise gain of 8.1.

The graph in Figure 11B illustrates the use of an improved cubic phase region wave surface coding optic. The system of its cubic phase region is constant over the +/- 1.0 mm square aperture region, as the narrowed F / 19 system in Figure 10B has adequate performance for light rays within a 2 mm diameter aperture. Or has zero phase. This zero-phase region corresponds to the aperture of the narrowed F / 19 system.

The zero-phase region can be formed into a circular or other geometric shape very easily, depending on the application and processing used. The square aperture is more in harmony with the perpendicularly separable nature of the system in the cubic phase region than in the inseparable circular region.

The parameters of the cubic phase region system of FIG. 11B were designed to be less susceptible to off-axis misfocus aberrations, similar to the prior art tertiary phase system of FIG. 11A. This leads to a result that the OPD from the peak to the valley on the axis is also about 9.5λ. The contour plot of the exit pupil on the left of Figure 11B shows zero phase near the center of the aperture when compared to the contour plot derived from the prior art cubic phase system that is not optically constant over any region of the aperture. It clearly shows the large area it has. The MTF of the angle-of-view function for the improved cubic phase region system before image processing seems to be basically constant. The resulting MTF heights from the improved cubic phase region system are also those obtained from the spatial frequency band limit of the 7.6 micron detector, or from the prior art tertiary phase system below 65 lb / mm. Much higher than.

The noise gain of the 2D digital filter required to match the filtered MTF performance to that of the diffraction-limited system has a value of about 3.2 in the improved cubic phase region system. As a result, the improved cubic phase region system produces near-ideal performance for controlling field-dependent aberrations, and the noise gain of the digital filter derived from the prior art system is also a factor (8.1 / 3.2). That is, it drops significantly at about 2.5. As a result, the power of additional noise in the final image after image processing 110 will be 2.5 times greater in the prior art system than in the wave surface coding system in the improved cubic phase region.

This significant reduction in noise gain will result in significantly less noisy final images from the improved wave surface coding optics when compared to prior art optics. Alternatively, with respect to a certain amount of noise gain, the improved wave surface coding optics can control a much greater degree of misfocus than prior art optics allow.

Although not shown, this lens system, when modified by wave surface coding, also significantly corrects misfocus resulting from color and temperature related effects, while at the same time reducing system tolerances to manufacturing and assembly errors. Make it smaller.

<figref num="1">It is a figure which shows the wave surface coding imaging system by the prior art.</figref><figref num="2">It is a figure which shows the 1D plot of the cubic phase function of the wave plane coding of FIG. 1 and the contour line plot of the 2D representation of this function.</figref><figref num="3">It is a figure which shows MTF as a function of misfocus for the system which does not have a wave surface coding, and the system which has the conventional wave surface coding cubic phase function of FIG.</figref><figref num="4">It is a figure which shows the ray path for the system which does not have a wave surface coding, and the system which has the conventional wave surface coding cubic phase function shown in FIG.</figref><figref num="5A">It is a figure which shows the ray path about the linear region phase function by this invention.</figref><figref num="5B">It is a figure which shows the ray path about the cubic region phase function by this invention.</figref><figref num="6">It is a figure which shows the 1D plot of the phase profile of the linear region and the cubic region of 5a and 5b, and the contour plot of the 2D representation of these wave surface coding functions.</figref><figref num="7">It is a figure which shows MTF as a function of misfocus for the system which does not have a wave surface coding, and the system which has the optical system of the linear region and the cubic region of FIGS. 5a and 5b.</figref><figref num="8">It is a figure which shows the contour plot of the improved inseparable phase function by this invention, the plot of a 1D slice passing through an inseparable phase function, and MTF as a function of misfocus about an inseparable cubic sector phase function.</figref><figref num="9">It is a figure which shows the drawing of the conventional Cooke triple lens.</figref><figref num="10A">It is a figure which shows the contour plot of the exit pupil and MTF as a function of the corresponding angle of view for the Cooke triple lens of FIG. 9 of a full aperture.</figref><figref num="10B">It is a figure which shows the contour plot of the exit pupil and MTF as a function of the corresponding angle of view about the Cooke triple lens of FIG. 9 which was narrowed down.</figref><figref num="11A">It is a figure which shows the contour plot of the exit pupil and MTF as a function of the corresponding angle of view about the 3rd order phase wave surface coding system of the prior art of FIG.</figref><figref num="11B">It is a figure which shows the contour plot of the exit pupil and MTF as a function of the corresponding angle of view about the wave surface coding system of the improved cubic region of FIG.</figref>