Moving display

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to electrical and electronic displays and, more particularly, to a type of display in which a display zone is scanned repeatedly by one or more arrays of lights to create the illusion of an image floating in space.

Displays of this type are known. Illustrative examples include those described by Lock in UK Patent Application No. GB 2 093 617 A and by Belcher et al. in US Patent No. 5,302,965, both of which are incorporated by reference for all purposes as if fully set forth herein. Generally, these displays consist of a mobile, typically rotating, unit and a stationary unit. For example, in the displays of Lock and Belcher et al., the mobile unit in fact does only rotate with respect to the stationary unit. The mobile unit includes at least one array of light sources, typically light emitting diodes, oriented perpendicularly to the direction of motion of the mobile unit. As the mobile unit moves, the arrays of light sources sweep a path in a display zone. At each of several positions of the arrays within the display zone, different combinations of the light sources are illuminated. This creates the illusion of an image floating in space, with each light source at each position corresponding to one pixel of the image, and one column of pixels being displayed at each position. With appropriate sequencing of the illumination and extinction of the light sources, this image can be animated.

Displays of this kind suffer from two limitations. The first limitation relates to the accuracy with which the light sources can be positioned relative to the desired column positions. In known devices, the positions of the arrays are determined by measuring the position of the mobile unit as a whole, and inferring the positions of the arrays from this single measurement. For example, in one embodiment of Lock's display, the periphery of a slotted disk fixed to the stationary unit is scanned by an optical reading device fixed to the rotating unit to measure the angular position of the rotating unit relative to the stationary unit. The accuracy and stability of the inferred (nominal) positions of the arrays relative to their actual positions then depends on the accurate alignment and mechanical stability of the mobile unit. In principle, only one array need be used to scan the display zone. In practice, there is a tradeoff between number of arrays, scan speed, and illumination level; and several arrays are needed to achieve an adequate level of illumination and an adequate scan speed. Small inaccuracies in the alignment of the mobile unit, and mechanical instability of the mobile unit, cause the arrays to be in positions other than their nominal positions as the mobile unit move. Because the light sources of the arrays are tumed on and off sequentially as though the arrays were in their nominal positions, the resulting image is blurred.

A second limitation of these kinds of arrays relates to the limited amount of data that can be stored on the mobile unit. Typically, the mobile unit stores only as much data as is needed to display a small number of images, with a much larger store of data being stored in the stationary unit. In the display of Belcher et al., for example, data for new images may be transmitted from the stationary unit to the mobile unit, but only at a rate much slower than the rate at which the corresponding signals must be transmitted to the moving arrays. This limits the extent to which these displays may be used to display animated images.

There is thus a widely recognized need for, and it would be highly advantageous to have, a display, of the type in which a display zone is scanned repeatedly by one or more arrays of lights to create the illusion of an image floating in space, in which control signals are transmitted to the arrays according to their actual positions, rather than their nominal positions, and at a rate fast enough to support animation of the floating image.

SUMMARY OF THE INVENTION

According to the present invention there is provided a display of the type in which a plurality of arrays of light sources are moved successively among a plurality of positions in a common plane of motion to perform a repetitive scanning of a display zone, including: (a) a mechanism for providing each array with data to display at each one of the positions when the array has arrived at the each one of the positions; and (b) for each array, a mechanism for detecting an arrival of the array at the each one of the positions.

According to the present invention there is provided a display for displaying an image in a display zone, including: (a) a stationary unit; (b) a mobile unit, including at least one array of light sources, for moving the at least one array of light sources successively among a plurality of positions along a path to perform a repetitive scanning of the display zone; (c) a medium for storing data to be displayed by the at least one array at each of the positions, the medium being geometrically congruent with the path; (d) a mechanism, rigidly attached to the stationary unit, for securing the medium on the stationary unit; and (e) a mechanism, rigidly attached to the mobile unit, for reading the data as the moving unit moves.

According to the present invention there is provided, in a system wherein a static image is displayed by moving at least one illuminator successively among a plurality of positions, data to be displayed at each of the positions being provided to each of the at least one illuminator at a certain static refresh frequency, a method for displaying an image moving at a constant speed, including the steps of: (a) determining a moving refresh frequency, based on the static refresh frequency and on the constant speed; and (b) providing the data to each of the at least one illuminator at the moving refresh frequency.

According to a first aspect of the present invention, related to a display in which the arrays move among a set of coplanar positions, each array is provided with a mechanism for sensing when it arrives at one of the positions, and the stationary unit is configured to transmit to each array, when it arrives at a certain position, only the data that is to be displayed by the array at that position. In the examples of preferred embodiments described herein, the positions are along the circumference of a circle, although the scope of the present invention includes displays in which the arrays move in any coplanar sequence of array positions. In one embodiment of this aspect of the present invention, the stationary unit is provided with a flat surface bearing a circular pattern of apertures, each aperture corresponding to one sequential position of the arrays, and is also provided with an illumination source on the opposite side of this surface from the mobile unit; and each array is provided with an optical sensor to sense when it transits from one aperture to the next, based on the periodic alternation of the presence and absence of light transmitted through the flat surface. A control system in the stationary unit continuously interrogates the arrays and, upon determining that a given array has arrived at a certain position, transmits to that array the data to be displayed at that position. In another embodiment of this aspect of the present invention, the stationary unit is provided with a circular ensemble of conductive plates, each plate corresponding to one sequential position of the arrays, and is also provided with electrical connections from a memory device to the conductive plates, whereby each conductive plate is provided with electrical signals corresponding to the data to be displayed at the corresponding position. Each array is provided with a pair of parallel conductive plates, disposed so that as that array sweeps past a particular position, the conductive plate of the circular ensemble that corresponds to that position is sandwiched between the parallel plates attached to the array, forming a capacitively coupled link between the memory device and the array, so that the data to be displayed at that position is transmitted to the array.

According to a second aspect of the present invention, in which the arrays move repetitively along a certain path as the mobile unit moves with respect to the stationary unit, the stationary unit includes a mechanism for holding a data storage medium, such as a magnetic storage medium, that is geometrically congruent with the path followed by the arrays, and the mobile unit includes a mechanism, such as a magnetic read head, for reading the data stored on the data storage medium as the mobile unit moves past the data storage medium. The scope of the present invention includes all such paths, with geometric congruence being established by the use of flexible magnetic tape, shaped to follow the path, as the data storage medium. For example, if the mobile unit moves the arrays back and forth along a linear path, the magnetic tape is stretched out parallel to the path. Nevertheless, in the preferred embodiment of this aspect of the present invention, the path is circular, the mobile unit rotates on an axis relative to the stationary unit, and the data storage medium is cylindrical, for example, a floppy disk, and is secured on the stationary unit concentric with the axis of rotation. With an appropriate ordering of the data on a cylindrical storage medium, as described below, data to be displayed by each array at each position may be transferred to that array in real time, allowing the arrays to have direct access to the full data set to be displayed.

It will be appreciated that, within the preferred embodiment of the second aspect of the present invention, the cylindrical data storage medium need not be magnetic. For example, the data storage medium may be a compact disk, read by an optical read head in the mobile unit.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein: <ul id="ul0001" list-style="none" compact="compact"><li>FIG. 1 is a partial perspective view of a first embodiment of the present invention;</li><li>FIG. 2 is a schematic block diagram of the electronic circuitry of the embodiment of FIG. 1;</li><li>FIG. 3 is a partial perspective view of a second embodiment of the present invention;</li><li>FIG. 4 is a schematic block diagram of the electronic circuitry of the embodiment of Fig. 3;</li><li>FIG. 5 is a vertical cross section of a third embodiment of the present invention;</li><li>FIG. 6 is a vertical cross section of a fourth embodiment of the present invention.</li></ul>

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is of a display, of the type that creates the illusion of an image floating in space, in which the arrays that create the illusion are provided with display data in a manner that eliminates the blurring of the image and that enables full animation of the image.

The principles and operation of a display according to the present invention may be better understood with reference to the drawings and the accompanying description.

Referring now to the drawings, Figure 1 is a partial perspective view of a first preferred embodiment of the present invention. In this embodiment, the stationary unit includes an opaque barrier <b>20</b> coextensive with one surface thereof, and the mobile unit, which rotates at a uniform angular velocity about an axis <b>30</b> relative to the stationary unit, includes four linear arrays <b>10</b> of light emitting diodes (LEDs) <b>12</b>. As the mobile unit rotates, ends <b>11</b> of arrays <b>12</b> move in a circular path that is slightly displaced from and parallel to barrier <b>20</b>. The stationary unit also includes an illumination source <b>26</b> on the side of barrier <b>20</b> opposite the mobile unit. Barrier <b>20</b> includes a plurality of evenly spaced apertures <b>22</b> arrayed in a circle that is directly opposite to the circular path of motion of ends <b>11</b> of arrays <b>12</b>, at positions corresponding to the pixel columns of the floating images displayed by means of LEDs <b>12</b>. Between one pair of evenly spaced apertures <b>22</b> is an initial position aperture <b>24</b>. Each array <b>12</b> includes an optical sensor <b>14</b> on end <b>11</b> thereof. Optical sensors <b>14</b> are used to detect light from source <b>26</b> that traverses barrier <b>20</b> via apertures <b>22</b> and <b>24</b> to indicate to each array <b>12</b> the arrival of array <b>12</b> at a position opposite each of apertures <b>22</b> and <b>24</b>.

Note that only the parts of this embodiment that are relevant to a description of the present invention are shown in Figure 1. So, for example, the mechanism for rotating the mobile unit at a uniform angular velocity about axis <b>30</b> relative to the stationary unit is not shown. The mechanisms taught by Lock and by Belcher et al. are readily adapted to this purpose by one ordinarily skilled in the art. If the mechanism taught by Lock is used, then opaque barrier <b>20</b> forms the upper surface of the stationary unit.

It will be appreciated that the principle upon which the embodiment of Figure 1 is based is the discrete illumination, along a surface of the stationary unit, of positions along the path followed by arrays <b>12</b> that correspond to the pixel columns of the images to be displayed. So, for example, instead of source <b>26</b> and apertures <b>22</b> and <b>24</b>, the stationary unit may include a circular ensemble of LEDs in the surface thereof past which ends <b>11</b> of arrays <b>12</b> move.

Figure 2 is a schematic block diagram of the electronic circuitry that drives arrays <b>10</b>, under the control of a microprocessor-based control unit <b>60</b>. Data corresponding to the images to be displayed is stored in a memory unit <b>62</b>. Control unit <b>60</b> addresses this data via an address bus <b>64</b>. The addressed is provided to control unit <b>60</b> via a data bus <b>66</b>. Control unit <b>60</b> and memory <b>62</b> are located in the stationary unit.

The mobile unit includes, for each array <b>10</b>, a corresponding control module <b>40</b>. Control module <b>40</b> includes a pulse selector <b>42</b>, a counter <b>44</b>, a flip flop <b>46</b>, a shift register <b>48</b> and a register driver <b>50</b>. Communication links between control modules <b>40</b> and control unit <b>60</b>, symbolized in Figure 2 by the vertical lines and the vertical double arrow that connect control unit <b>60</b> and control module <b>40</b>, are provided as taught by Lock and by Belcher et al. For clarity, only one control module <b>40</b> is shown in Figure 2.

Whenever sensor <b>14</b> arrives opposite aperture <b>22</b> or <b>24</b>, light traversing barrier <b>20</b> via aperture <b>22</b> or <b>24</b> causes an electrical pulse to be sent to counter <b>44</b>. Pulse selector <b>42</b> distinguishes a pulse due to an arrival of sensor <b>14</b> opposite aperture <b>24</b> from pulses due to arrivals of sensor <b>14</b> opposite apertures <b>22</b>, on the basis of the time interval between a pulse due to an arrival of sensor <b>14</b> opposite aperture <b>24</b> and the immediately preceding pulse being half of the time interval between arrivals of sensor <b>14</b> opposite adjacent apertures <b>22</b>. Upon detecting a pulse due to an arrival of sensor <b>14</b> opposite aperture <b>24</b>, pulse selector <b>42</b> resets counter <b>44</b> to the initial state thereof. Upon detecting a pulse due to an arrival of sensor <b>14</b> opposite one of apertures <b>22</b>, pulse selector <b>42</b> increases the count stored in counter <b>44</b> by one unit. Thus, the angular position of array <b>10</b> relative to the stationary unit is indicated by the state of counter <b>44</b>. Each electrical pulse from sensor <b>14</b> also sets flip flop <b>46</b> to the active state thereof and causes data transfer from shift register <b>48</b> to register driver <b>50</b> which drives LEDs <b>12</b> of array <b>10</b>.

Periodically, at a rate higher (typically twice as high) than the time interval between arrivals of sensors <b>14</b> at adjacent apertures <b>22</b>, control unit <b>60</b> interrogates flip flop <b>46</b>. If flip flop <b>46</b> is in its active state, control unit <b>60</b> reads the state of counter <b>44</b> to determine the angular position of array <b>10</b>. Control unit <b>60</b> then reads data corresponding to that angular position from memory <b>62</b>, transfers these data to shift register <b>48</b>, and resets flip flop <b>46</b>.

Figure 3 is a partial perspective view of a second embodiment of the present invention. In this embodiment, the surface of the stationary unit, past which the mobile unit rotates about axis <b>30</b>, is provided with a circular ensemble of conductive plates <b>70</b>. Each plate <b>70</b> is located at a point corresponding to a pixel column of the images to be displayed. Each array <b>10</b> is provided, at end <b>11</b> thereof, with a pair of conductive plates <b>72</b> that straddle conductive plates <b>70</b>, providing, at each conductive plate <b>70</b> so straddled, a capacitive link between array <b>10</b> and the stationary unit. Each conductive plate <b>70</b> is connected by a wire <b>76</b> to control unit <b>60</b>, whereby control unit <b>60</b> transmits to each conductive plate <b>70</b> only data to be displayed in the corresponding column of image pixels.

Figure 4 is a schematic block diagram of the electronic circuitry that drives arrays <b>10</b> in the embodiment of Figure 3, again under the control of control unit <b>60</b> in the stationary unit. There are an even number of conductive plates <b>70</b>, each conductive plate <b>70</b> being connected to control unit <b>60</b> by wires <b>76</b>. Alternate conductive plates <b>70</b> are connected to control unit <b>60</b> via inverters <b>78</b>. For clarity, only 7 conductive plates <b>70</b> are shown in Figure 4.

The mobile unit includes, for each array <b>10</b>, a corresponding control module <b>80</b>, for receiving signals through the capacitively coupled links between conductive plates <b>70</b> and <b>72</b>. Control module <b>80</b> includes a demodulator <b>82</b>, a data packet detector <b>84</b>, a shift register <b>86</b>, a phase lock loop <b>90</b>, a pulse shaper <b>98</b> and a register driver <b>100</b>. Phase lock loop <b>90</b> in turn includes a phase detector <b>92</b>, a low pass filter <b>94</b> and a voltage controlled oscillator <b>96</b>. For clarity, only one mobile unit <b>80</b> is shown in Figure 4.

Control unit <b>60</b> transmits data to conductive plates <b>70</b> as a modulated carrier wave. Every other conductive plate <b>70</b> receives this modulated carrier wave, via inverter <b>78</b>, as an inverted wave. The modulated carrier wave is transmitted, via the capacitively coupled link between conductive plates <b>70</b> and <b>72</b>, to demodulator <b>82</b> and phase lock loop <b>90</b>. Phase lock loop <b>90</b> supplies demodulator <b>82</b> with a signal identical to the carrier wave, except for being 90° out of phase with the carrier wave: the reference signal leads uninverted modulated signals (signals that do not traverse one of inverters <b>78</b>) by 90° and lags inverted modulated signals (signals that do traverse one of inverters <b>78</b>) by 90°. Demodulator <b>82</b> uses the reference signal from phase lock loop <b>90</b> to recover the data from the modulated signals and pass the data on to data packet detector <b>84</b>.

Data are transmitted in packets, with each packet including a preamble, a postamble, and, between the preamble and the postamble, bits corresponding to the sequence of LEDs <b>12</b> to be tumed on and off at the angular position of each conductive plate <b>70</b>. Several (preferably at least three) packets are transmitted in the time that it takes for an array <b>10</b> to sweep past one conductive plate <b>70</b>, so that the transmission of data to arrays <b>10</b> need not be exactly synchronized with the angular positions of arrays <b>10</b>. When data packet detector <b>84</b> detects the arrival of a complete packet, including the preamble and the postamble, data packet detector <b>84</b> strips the preamble and the postamble from the packet and passes on the data to shift register <b>86</b>, along with a synchronization signal.

The output of low pass filter <b>94</b>, in addition to being passed to voltage controlled oscillator <b>96</b>, is passed to pulse shaper <b>98</b>. Whenever a capacitively coupled link is broken with one conductive plate <b>70</b> and established with the next conductive plate <b>70</b>, the polarity of the output of low pass filter <b>94</b> changes. Pulse shaper <b>98</b> transforms this polarity change to a pulse, which triggers register driver <b>100</b> to write the data stored in shift register <b>86</b> to array <b>10</b>.

The capacitive communications link described herein for transmitting data from control unit <b>60</b> to arrays <b>10</b>, including wires <b>76</b> and conductive plates <b>70</b> and <b>72</b>, is one illustrative example of a multichannel communications link between control unit <b>60</b> and arrays <b>10</b>. The scope of the present invention includes all equivalent links, for example, optical links and magnetic induction links.

In both the first embodiment and the second embodiment, typical rotational speeds range from 100 rpm to 900 rpm, and the number of pixel columns in the image typically range between 64 and 512. Thus, in the first embodiment, typically there are between 64 and 512 apertures <b>22</b> in opaque barrier <b>20</b>, and in the second embodiment, typically there are between 64 and 512 conductive plates <b>70</b>.

Figure 5 is a vertical cross section through a third embodiment of the present invention, illustrating the second aspect of the present invention. In this embodiment, a mobile unit <b>100</b> includes two linear arrays <b>110</b> of LEDs <b>112</b> at the ends of oppositely directed arms <b>114</b> that extend from a central hollow cylindrical shaft <b>116</b>. Mounted above shaft <b>116</b> is a control unit <b>118</b>. To the end of shaft <b>116</b> opposite arms <b>114</b> is rigidly attached a floppy disk drive <b>120</b> that includes a magnetic read head <b>122</b>, a radial positioning drive <b>124</b>, and other standard components not shown in Figure 5. An electrical connection (not shown) is provided between control unit <b>118</b> and disk drive <b>120</b> through the hollow interior of shaft <b>116</b>. This embodiment also includes a stationary unit <b>105</b>, which includes a sleeve <b>132</b>, that is mounted on a base <b>130</b>, and that contains bearings <b>134</b> within which shaft <b>116</b> is rotatably mounted. Stationary unit <b>105</b> also includes a motor <b>136</b>, mounted on base <b>130</b>, that drives the rotation of shaft <b>116</b> by means of a drive belt <b>138</b> and a pulley <b>140</b>.

A floppy disk <b>150</b>, within a floppy disk case <b>152</b>, is mounted within disk drive <b>120</b> and held stationary therein by a pressure unit <b>142</b> mounted on spindle <b>144</b> that is attached to base <b>130</b> concentric with shaft <b>116</b>. As the mobile unit, including disk drive <b>120</b>, rotates, pressure unit <b>142</b> holds floppy disk <b>150</b> stationary. Thus, the reading of floppy disk <b>150</b> is accomplished in a manner opposite to the conventional manner. Instead of floppy disk <b>150</b> rotating within case <b>152</b> and disk drive <b>120</b>, floppy disk <b>150</b> remains stationary, while disk drive <b>120</b> and case <b>152</b> rotate around floppy disk <b>150</b>.

Figure 6 is a vertical cross section through a fourth embodiment of the present invention, also illustrating the second aspect of the present invention. The embodiments of Figures 5 and 6 share most of their components, and components so shared are designated by identical reference numerals in Figures 5 and 6. In the embodiment of Figure 6, mobile unit <b>100</b> includes a central hollow cylindrical sleeve <b>160</b> atop which are mounted both disk drive <b>120</b> and control unit <b>118</b>. Stationary unit <b>105</b> includes a solid central shaft <b>170</b> about which sleeve <b>160</b> is rotatably mounted on bearings <b>172</b>. Motor <b>136</b> drives the rotation of sleeve <b>160</b> by means of drive belt <b>138</b> and a pulley <b>162</b>. Pressure unit <b>142</b> that holds floppy disk <b>150</b> in place is mounted on top of shaft <b>170</b>. Otherwise, the embodiment of Figure 6 is structurally and functionally identical to the embodiment of Figure 5.

To maximize the speed at which data are read from floppy disk <b>150</b>, the data to be displayed in successive pixel columns are interleaved. For example, if L linear arrays are used to display N pixel columns, with N being an integral multiple of L, the order of data storage is: <tables id="tabl0001" num="0001"><table frame="all"><tgroup cols="4" colsep="1" rowsep="0"><colspec colnum="1" colname="col1" colwidth="39.37mm" /><colspec colnum="2" colname="col2" colwidth="39.37mm" /><colspec colnum="3" colname="col3" colwidth="39.37mm" /><colspec colnum="4" colname="col4" colwidth="39.37mm" /><tbody valign="top"><row><entry namest="col1" nameend="col1" align="left">column 1</entry><entry namest="col2" nameend="col2" align="left">column N/L + 1</entry><entry namest="col3" nameend="col3" align="left">column 2N/L + 1  ...</entry><entry namest="col4" nameend="col4" align="left">column N - N/L + 1</entry></row><row><entry namest="col1" nameend="col1" align="left">column 2</entry><entry namest="col2" nameend="col2" align="left">column N/L + 2</entry><entry namest="col3" nameend="col3" align="left">column 2N/L + 2  ...</entry><entry namest="col4" nameend="col4" align="left">column N -N/L + 2</entry></row><row><entry namest="col1" nameend="col1" align="left">...</entry><entry namest="col2" nameend="col2" /><entry namest="col3" nameend="col3" /><entry namest="col4" nameend="col4" /></row><row rowsep="1"><entry namest="col1" nameend="col1" align="left">column N/L</entry><entry namest="col2" nameend="col2" align="left">column 2N/L</entry><entry namest="col3" nameend="col3" align="left">column 3N/L    ...</entry><entry namest="col4" nameend="col4" align="left">column N</entry></row></tbody></tgroup></table></tables> For example, in an embodiment, such as those of Figures 5 and 6, that has 2 linear arrays <b>110</b> of LEDs <b>112</b>, if the image to be displayed has 64 columns, then the columns are stored in the order 1, 33, 2, 34, 3, 35, ... , 31, 63, 32, 64. The first two columns read from floppy disk <b>150</b> then are columns 1 and 33, which are in fact the first two columns to be displayed, because when one linear array <b>110</b> is at a position corresponding to pixel column 1, the other linear array <b>110</b> is diametrically opposite the first linear array <b>110</b>, at a position corresponding to pixel column 33. It will be readily apparent, to one ordinarily skilled in the art, how to synchronize the reading of floppy disk <b>150</b> with the display of data on linear arrays <b>110</b> at the various positions thereof.

As noted above, the cylindrical data storage medium of the preferred embodiment of the second aspect of the present invention may be an optical storage medium such as a compact disk. Figures 5 and 6 also may be understood to represent this variant of the present invention, with reference numeral <b>150</b> designating a compact disk, reference numeral <b>120</b> designating a compact disk drive, and reference numeral <b>122</b> designating an optical read head.

The embodiments of the present invention described herein are well-suited to creating the illusion of an image floating in a single position in space. These embodiments also are well-suited to creating the illusion of an image moving at a constant velocity in space, provided appropriate care is taken to avoid spatial aliasing. This will now be explained in terms of specific examples.

The reference example is the display of a static image using the first preferred embodiment of the present invention, with 180 apertures <b>22</b>. The static image has 180 columns, one per aperture <b>22</b>, with each column occupying 2° of arc length. The mobile unit rotates at 10 revolutions per second, so that the static image is scanned by LED arrays <b>10</b> 40 times per second. Each array <b>10</b> occupies the 2° arc length of each column for 1/1800 seconds. Therefore, the refresh rate at which new display data are provided to each array 10 is 1800 Hz.

Now suppose that it is desired to make the floating image rotate in the same direction as the mobile unit, only more slowly. Specifically, suppose that it is desired that the floating image rotate once every 4.5 seconds, i.e., at a constant angular speed of 80° per second. The naive way to implement this would be to simply translate 80° per second into 40 columns per second. For the first 1/40 second, data are transferred to register drivers <b>50</b> of arrays <b>10</b> as in the static case. For the second 1/40 second, data are transferred to register drivers <b>50</b> of arrays <b>10</b> in a manner corresponding to a 2° shift of the image: data that were formerly transferred to arrays <b>10</b> when they are opposite aperture <b>22</b> whose angular coordinate is 0° now are transferred to arrays <b>10</b> when they are opposite aperture <b>22</b> whose angular coordinate is 2°, and so on.

The problem with this naive implementation is that it leads to spatial aliasing. Consider, for example, an array <b>10</b> starting at angular position 0° and displaying, for the first 1/1800 seconds, data of image column number 1. For the second 1/1800 seconds, this array <b>10</b> is at angular position 2° and displays data of image column number 2. For the 45th 1/1800 seconds, this array <b>10</b> is at angular position 88° and displays data of image column number 45. But now, 1/40 of a second having elapsed, the data transfer is shifted 2° in the direction of rotation. As a result, for the 46th 1/1800 seconds, this array <b>10</b>, being at angular position 90°, again displays data of image column number 45. In practice, this spatial aliasing produces a number of visible seams in the rotating image, the number of seams being equal to the number of arrays <b>10</b>. The same effect is observed if the floating image rotates in the direction opposite to the direction in which the mobile unit rotates, the effect in this case being caused by arrays <b>10</b> skipping image columns rather than duplicating image columns.

The fundamental cause of this spatial aliasing is that, although the image columns are 2° wide in the rotating coordinate system of the image, they are not 2° wide in the stationary coordinate system of apertures <b>22</b>. The way to overcome this spatial aliasing is to break the connection between the angular positions marked by apertures <b>22</b> and the angular widths of the displayed image columns.

Suppose that an array <b>10</b> starts, along with the trailing edge of an image column, at angular position 0° at time 0. For how long should the data of this image column be displayed? Denote this unknown time by <i>t</i>. Array <b>10</b> moves at 3600° per second. The leading edge of the image column starts at an angular position of 2° and moves at 80° per second. The data of the image column should be displayed just long enough for array <b>10</b> to catch up to the leading edge of the image column. At that point, the angular position of array <b>10</b> is 3600<i>t</i> and the angular position of the leading edge of the image column is 2 + 80<i>t</i>. Solving the equation 3600<i>t</i> = 2 + 80<i>t</i> for <i>t</i> gives <i>t</i> = 1/1760 seconds. The straightforward way to eliminate aliasing is to provide data to arrays <b>10</b> at a slower refresh rate of 1760 Hz instead of the base refresh rate of 1800 Hz. Note that under this method, the signals from sensors <b>14</b> are used, not to determine the angular positions of arrays <b>10</b>, but to provide a real-time measure of the base refresh frequency, which may vary about the nominal 1800 Hz value, depending on the accuracy with which the mobile unit is aligned and on the mechanical stability of the mobile unit. Frequency synthesis methods for synthesizing the desired refresh frequency from the base refresh frequency, based on the desired rotational speed of the image, are well-known in the art and need not be detailed here.

It will be appreciated that this method for overcoming spatial aliasing is applicable to any system in which one or more illuminators, such as LED arrays <b>10</b>, are moved successively among a series of predetermined positions to display a floating and moving image.

While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made.