WO2012120470A1

WO2012120470A1 - Stereographic viewing with extended depth of field

Info

Publication number: WO2012120470A1
Application number: PCT/IB2012/051089
Authority: WO
Inventors: Saar Wilf; Alex Alon; Yoav Yadin; Yariv HADDAD
Original assignee: Optika Amuka (A.A.) Ltd.
Priority date: 2011-03-10
Filing date: 2012-03-08
Publication date: 2012-09-13

Abstract

Apparatus (20) for viewing a stereographic display (24), which presents different, respective images for viewing by a right eye and a left eye of a viewer. The apparatus includes spectacles (26), which include right and left optical filters (34) to select the respective images for viewing by the right and left eyes. One or more optical phase plates (36) are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance a depth of field of the eyes. A digital image processor (30) pre-processes the images presented on the stereographic display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

Description

STEREOGRAPHIC VIEWING WITH EXTENDED DEPTH OF FIELD

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application 61/451,133, filed March 10, 2011, which is incorporated herein by reference. FIELD OF THE INVENTION

The present invention relates generally to optical systems and methods, and particularly to enhancement of stereographic image displays.

BACKGROUND

Stereopsis is the perception of depth that the human brain derives from binocular vision, based on the different projections of a scene onto the retinas of the two eyes. Stereopsis depends on vergence of the eyes in order to maintain a single binocular image while inducing a sense of depth. In vergence, the eyes move simultaneously in opposite directions, rotating around a vertical axis so that the projection of the image is in the centre of the retina in both eyes. To look at a nearby object, the eyes rotate towards each other (convergence), whereas for an object farther away they rotate away from each other (divergence).

Stereographic three-dimensional (3D) imaging operates by manipulation of stereopsis, by providing each eye with a slightly different image. The brain interprets the differences as though they resulted from parallax provided by the different positions of the two eyes in the head and thus perceives a 3D image. Most stereographic systems use special glasses or goggles to cause the left and right eyes to see different images. Viewing stereographic imaging can be visually tiring and causes headache in some viewers.

A number of attempts have been made to alleviate the visual fatigue that is associated with stereographic viewing. For example, European Patent Application EP2309310, whose disclosure is incorporated herein by reference, describes 3D spectacles for viewing three- dimensional image data via a left image and a right image at a display viewing distance. The spectacles are arranged to admit only the left image to the left eye and only the right image to the right eye. In a nominal eye configuration the eyes are accommodated at the display viewing distance by a nominal eye-convergence and a nominal eye lens focal length. The spectacles have optical elements for changing optical radiation from the 3D display in order to modify the nominal eye configuration to a compensated eye configuration in accordance with depth to be perceived in the 3D image data. A 3D image processing device has an adjustment unit for adjusting the optical elements of the spectacles. The compensated eye configuration is said to be similar to an intended or natural eye configuration, which is less fatiguing and more comfortable for the viewer.

Depth of field (DOF), also referred to as depth of focus, is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. The term is used in reference both to imaging devices and systems, such as cameras, and to human vision. Various sorts of lenses and imaging systems have been developed for extending the depth of field.

For example, U.S. Patent Application Publication 2007/0236769, whose disclosure is incorporated herein by reference, describes an imaging arrangement and method for extended depth of focus. The imaging arrangement comprises an imaging lens having a certain effective aperture, and an optical element associated with the imaging lens. The optical element is configured as a phase-affecting, non-diffractive optical element defining a spatially low- frequency phase transition. The optical element and the imaging lens define a predetermined pattern formed by spaced-apart, substantially optically-transparent features of different optical properties. The position of at least one phase transition region of the optical element within the imaging lens plane is determined by at least a dimension of the effective aperture.

SUMMARY

Embodiments of the present invention that are described hereinbelow provide improved systems, devices and methods for stereographic imaging.

There is therefore provided, in accordance with an embodiment of the present invention, apparatus for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer. The apparatus includes spectacles including right and left optical filters, which are configured to be interposed respectively in front of the right and left eyes of the viewer so as to select the respective images for viewing by the right and left eyes. One or more optical phase plates are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles. A digital image processor is configured to pre-process the images presented on the stereographic display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

In a disclosed embodiment, the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance. In one embodiment, the stereographic display is located at a given screen distance from the viewer and presents objects in the images at a virtual object distance, which is different from the screen distance, and the one or more optical phase plates include a lens configured to compensate for a difference between the screen distance and the virtual object distance. Additionally or alternatively, the one or more optical phase plates are adjustable responsively to the screen distance.

In disclosed embodiments, the spectacles are configured to form images in the eyes with a point spread function (PSF) that is determined by the one or more optical phase plates, and the digital filter is selected responsively to the PSF. The digital filter may include a convolution kernel that is inverse to the PSF. Typically, application of the digital filter to the images causes overshoot artifacts at edges in the images, and the digital image processor may be configured to apply an additional operation to the filtered images so as to reduce the overshoot artifacts. In one embodiment, the stereographic display is located at a given screen distance from the viewer, and objects in the images presented on the stereographic display appear to the viewer to be located at respective virtual object distances, which are different from the screen distance, and the digital image processor is configured to vary the digital filter responsively to variations in the virtual object distances of the objects appearing in different images.

There are also provided, in accordance with an embodiment of the present invention, spectacles for viewing a stereographic display. The spectacles include right and left optical filters and one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined, cylindrically non-symmetrical and non-separable phase pattern selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles.

In disclosed embodiments, the cylindrically non-symmetrical and non-separable phase pattern is selected so that the depth of field is enhanced over a range of shifts of pupils of the eyes relative to the spectacles.

There are additionally provided, in accordance with an embodiment of the present invention, spectacles for viewing a stereographic display, which include right and left optical filters and one or more optical phase plates, which are positioned adjacent to the right and left filters and are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance. There is further provided, in accordance with an embodiment of the present invention, a method for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer. The method includes providing spectacles to be worn by the viewer. The spectacles include right and left optical filters and one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles. The images presented on the stereographic display are pre-processed by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

There is moreover provided, in accordance with an embodiment of the present invention, a method for viewing a stereographic display, which includes interposing right and left optical filters respectively in front of the right and left eyes of the viewer, and positioning, adjacent to the right and left filters, one or more optical phase plates having a predefined, cylindrically non- symmetrical and non-separable phase pattern selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles.

In one embodiment, the phase pattern is optimized so that a modulation transfer function (MTF) of the eyes engendered by the one or more optical phase plate is within a desired MTF range over a specified depth of field for multiple, different shifts of the pupils.

There is furthermore provided, in accordance with an embodiment of the present invention, a method for viewing a stereographic display, which includes interposing right and left optical filters respectively in front of the right and left eyes and positioning, adjacent to the right and left filters, one or more optical phase plates that are configured to introduce aberrations in the images seen by the right and left eyes, wherein the method includes selecting the aberrations so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

There is also provided, in accordance with an embodiment of the present invention, apparatus for stereographic imaging, including a display, which is configured to present different, respective images for viewing by a right eye and a left eye of a viewer. One or more optical phase plates are positioned in an optical path between the display and the right and left eyes and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the display.

In one embodiment, the display and the one or more optical phase plates are configured to be mounted on a head of the viewer. There is additionally provided, in accordance with an embodiment of the present invention, a method for stereographic imaging, which includes presenting on a display different, respective images for viewing by a right eye and a left eye of a viewer. One or more optical phase plates are positioned in an optical path between the display and the right and left eyes, the one or more optical phase plates having a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the display.

The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a schematic, pictorial illustration of a stereographic imaging system, in accordance with an embodiment of the present invention;

Fig. 2 is a schematic side view of stereographic imaging optics, in accordance with an embodiment of the present invention;

Fig. 3 is a plot of modulation transfer function (MTF) for a stereographic imaging system with enhanced DOF, in accordance with an embodiment of the present invention;

Fig. 4A is a graphical representation of an optical phase plate used in enhancing DOF of stereographic imaging, in accordance with an embodiment of the present invention;

Fig. 4B is a numerical representation of the characteristics of the phase plate of Fig. 4A; Figs. 5 A and 5B are plots of MTF for different values of pupil shift in a stereographic imaging system with enhanced DOF, in accordance with an embodiment of the present invention;

Figs. 6A-6G are plots of the step response of the eye at different object distances in a stereographic imaging system with enhanced DOF, in accordance with an embodiment of the present invention; and

Figs. 7A-7C are simulated images comparing visual perception of image features in stereographic systems with and without DOF enhancement in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

OVERVIEW

When our eyes view an actual 3D scene, the depth of objects in the scene induces two depth-related phenomena: the binocular effect of vergence, as described above, and monocular accommodation, by which the lens of the eye changes its optical power in order to maintain a clear image (focus) on an object. In stereographic displays that are known in the art, however, the accommodation should be fixed at the distance of the eye from the display in order to maintain clear visual images, regardless of the simulated depth of displayed objects, while the vergence changes in response to the simulated depth. Thus, vergence may cause the brain to attempt to change the optical power of the eye in response to the perceived object depth, while the reflex of maintaining a clear image forces the accommodation to stay fixed at the display distance. These contradictory impulses can strain the eye's ciliary muscles and may cause headaches.

Embodiments of the present invention that are described hereinbelow enhance stereographic viewing in a way that can help to resolve the conflict of vergence and accommodation, by optically extending the depth of field (DOF) of the eyes. As a result, the eyes are able to accommodate at a depth that is concomitant with vergence at the simulated depth of objects on a stereographic display, while maintaining a clear, focused image notwithstanding the difference between the simulated object depth and the actual display distance.

Some embodiments of the present invention provide modified stereoscopic spectacles for extended DOF. Such spectacles normally comprise right and left optical filters, which are interposed respectively in front of the right and left eyes of the viewer so as to select the respective left and right images displayed on a stereographic screen. The term "filter" in this context should be understood broadly to include any and all optical means that are known in the art for selecting the right and left images, such as (but not limited to) color filters, polarization filters, and shutters that select right and left views in alternation.

The spectacles are modified by addition of one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance the DOF of the eyes while the eyes view the stereographic display through the spectacles. The term "phase plate" in this context refers to any optical element that modulates the phase of visible light that passes through it. Typically, for purposes of DOF enhancement in embodiments of the present invention, the phase plates have negligible refractive power of their own, although they may comprise a lens to compensate for the difference between the screen distance and the virtual object distance. Such phase plates may also affect the amplitude of the optical field, as long as the overall power of the light passing through the phase plates is not attenuated in such a way that inhibits viewing through the phase plates. The aberration of the optical phase plates tends to introduce a certain small focal blur into the images that are formed on the retinas of the eyes. This blur is characterized by a certain point spread function (PSF), which may be equivalently described in the frequency domain in terms of an optical transfer function (OTF). To compensate for this blur, in some embodiments, a digital image processor pre-processes stereographic images that are to be presented on the display, by applying a digital filter selected so as to compensate for the aberration of the optical phase plates. Typically, this digital filter is approximately inverse in its effect to the OTF of the phase plates.

Spectacles fit differently on different viewers, due to differences in facial structure and inter-pupillary distance. Furthermore, even for a single viewer, the eye's viewing angle may change, and the spectacles may shift in position during use. The inventors have found that when phase plates of types known in the art are used to achieve extended visual DOF, the DOF enhancement can be negated by even small displacements of the pupil of the viewer's eye relative to the phase plate. Therefore, in some embodiments of the present invention, the phase plates used in the stereographic spectacles have a predefined, cylindrically non-symmetrical and non-separable phase pattern that is selected so as to enhance the DOF of the eyes. This sort of phase pattern has been found to enhance DOF regardless of the direction and magnitude (within predefined limits) of shift between pupil and phase plate. An example of such a pattern is presented below. SYSTEM DESCRIPTION

Fig. 1 is a schematic, pictorial illustration of a stereographic imaging system 20, in accordance with an embodiment of the present invention. A viewer 22 views a display screen 24 through stereographic spectacles 26, with DOF enhancement as described below. The screen displays a sequence of left- and right-eye images, provided from a content source 28. An image processor 30 digitally pre-processes the images in order to compensate for the blur that is introduced by the DOF enhancement of the spectacles.

Image processor 30 typically comprises dedicated or programmable hardware logic. Alternatively or additionally, the processor 30 may comprise a general-purposes computer processor, which is programmed in software to carry out the functions (and specifically, digital image filtering) that are described herein. The software may be downloaded to image processor 30 over a network or, alternatively or additionally, may be stored in tangible, non-transitory media, such as optical, magnetic, or electronic memory. Although image processor 30 is shown in Fig. 1 in an on-line configuration, in which the digital pre-processing is executed in real time, during the display of the images, the image processor may alternatively or additionally process the images off-line, to prepare the processed images in advance.

Fig. 2 is a schematic side view of stereographic imaging optics used in spectacles 26, through which an eye 32 of viewer 22 views display screen 24 in accordance with an embodiment of the present invention. A filter 34, of any suitable type, selects either the left or right image that is to be seen by eye 32 and blocks out the other image. An optical phase plate 36 enhances the DOF of eye 32, as described below.

Optionally, spectacles 26 also include a lens 38, which increases or decreases the perceived distance of screen 24 from eye 32 to a distance in the expected vergence range of the stereographic images that are to be presented on the screen. In other words, lens 38 creates a virtual image of the screen at a greater or smaller distance from the eye (typically with the virtual image behind the screen, for example, with the virtual image in the range of 5-10 m with an actual screen distance of 70 cm). Lens 38 thus helps to reduce the conflict between vergence and accommodation, but it cannot eliminate the conflict altogether, since objects in the stereographic display are presented over a range of virtual object distances.

Although filter 34, phase plate 36, and lens 38 are shown in Fig. 2 as separate elements for the sake of conceptual clarity and simplicity, in practice these components may be combined into one or two optical elements. For example, filter 34 may be formed as a coating on phase plate 36 or lens 38. Additionally or alternatively, the optical properties of phase plate 36 and lens 38 may be combined in a single refractive or diffractive optical element (which may then be coated with filter 34). In fact, phase plate 36 and lens 38 may together be regarded simply as a phase plate with both refractive power and aberrations to provide the desired DOF enhancement. All such alternative implementations are considered to be within the scope of the present invention. OPTICAL DOF ENHANCEMENT

Phase plate 36 extends the focal range of eye 32 by introducing optical aberrations. In an optimal focusing system ("diffraction limited"), there is a distinct best focus point, called the hyperfocal point, with little or no aberration. At that point the PSF is smallest, and therefore objects located at the hyperfocal distance will appear sharp in the image. As the object moves away from the hyperfocal point, the PSF expands (due to the optical focus aberration), and the object appears more and more blurred. Phase plate 36 intentionally introduces additional aberrations, which reduce the dependence of the PSF on the focus aberration and give a PSF that is almost constant throughout a wide range of object distances. As noted earlier, image processor 30 may digitally apply an inverse PSF filter (or equivalently, an inverse OTF filter) to the images that are to be displayed on screen 24, resulting in a sharp final image in eye 32.

The image sharpness of system 20 can also be characterized in terms of its frequency response, as expressed by the modulation transfer function (MTF), which is the absolute value of the OTF. The MTF of an imaging system is related to the autocorrelation of the optical wavefront at the pupil of the system. As explained by Goodman, in Introduction to Fourier Optics (third edition, Roberts & Company, Englewood, New Jersey, 2005), the wavefront at the pupil is given by wherein represents

the pupil shape (circular in the human eye), W(x, y) is the phase error - the difference between the optical phase and a reference sphere converging to the ideal imaging point, k = 2π/λ and λ is the wavelength. The OTF as a function of spatial frequency in x- and y-directions (fx, fy) is then given by:

wherein A is the pupil area and Z_i is the distance between the lens and the image plane.

Denoting the overlap area between the two shifted pupil functions

, the OTF is then given by:

The hyperfocal point of a diffraction-limited optical system is characterized by W(x, y) = 0, and therefore When the object moves away from the

hyperfocal point (or, equivalently, when the image plane is shifted from the hyperfocal position), the wavefront error is given by a quadratic phase term,

wherein z_a is the distance between the pupil plane and the

actual image plane.

Enhanced depth of focus is achieved by adding an additional optical element near the pupil, referred to here as a phase plate, which adds an additional phase term to the wavefront error: Defining:

and

the OTF is then given by:

Phase plate 36 in system 20 is thus designed to increase the DOF of eye 32 by increasing the range of z_a for which

Fig. 3 presents plots of through-focus MTF (as a function of the defocus z_a— z ) for system 20, in accordance with an embodiment of the present invention. The MTF is calculated at a spatial frequency of 50 cycles/mm in the image plane (i.e., on the retina of eye 32), assuming cylindrical symmetry for the sake of simplicity. Since the system is cylindrically symmetrical, i.e., the OTF values for objects positioned on the

optical axis ("on axis") does not depend on the direction of the spatial frequency, i.e., For example,

and it is sufficient to examine one MTF graph, for

example MTF(f_x = SO, fy = θ), in order to appreciate the behavior of the system.

In Fig. 3, a reference plot 40 shows the MTF for an aberration-free focusing lens; a second plot 42 shows the MTF of a system including phase plate 36 with aberrations; and an enhanced plot 44 shows the MTF of the optical system used in plot 42 with the addition of a matching digital filter (inverse PSF) applied by image processor 30. The digital filter adds a gain of two at 50 cycles/mm. The focal length for all of the plots is 17 mm, and the pupil of eye 32 is assumed to be circular, with a diameter of 3.5 mm - typical for the human eye. The aberrations applied by phase plate 36 in this example, in terms of the Zernike fringe coefficients, are: Z9 = 0.31, Z16 = -0.11, and Z25 = -0.16.

As shown by plot 40, the aberration-free system has a distinctive best-focus point, with MTF rapidly decreasing as the object moves away from the optimal focus. By contrast, plot 42 exhibits relatively constant MTF across a wide range of object distances. Although the optical MTF of plot 42 is lower than the peak of plot 40, indicating a slight blur in the image, the addition of digital enhancement in plot 44 achieves a sharp image in the eye across a wide range of object distances. The digital filter applied by image processor 30 can be computed and applied in either the spatial domain or the frequency domain, as the inverse of the PSF or the OTF. An example of such a filter is presented below.

OVERCOMING PUPIL MISALIGNMENT

As explained earlier, it is difficult to achieve and to maintain precise alignment between the optical axes of spectacles 26 and the pupils of the eyes of viewer 22. Reasons for misalignment may include variations in head shapes and facial structure among different viewers, as well as movements of the eye of any given viewer (which may cover a range of several millimeters in pupil position). When the pupil moves with respect to phase plate 36, the effective phase impact on the eye changes accordingly. The possible range of the relative shifts between phase plate 36 and the pupil is large, and can be larger than the pupil size itself. In order for the system 20 to work satisfactorily in practice, it is desirable that spectacles 26 provide DOF enhancement for various pupil position.

The extended DOF criterion, taking into account pupil shift, can be expressed by the requirement that for every two-dimensional shift vector (s_x, Sy),

When relative shifts between the pupil and the phase plate are introduced, no cylindrically- symmetrical solution to this equation exists (except for a trivial constant phase, Wp (x, y) = const, over phase plate 36). In non-cylindrically-symmetrical cases, the MTF depends on the direction of the frequency vector, as well as on its magnitude. Although separable solutions can maintain high MTF values along the axes (i.e., for frequencies (fx, fy) = ( , 0) and (fx, fy) = (0, /)), such solutions still suffer from a rapid drop in the MTF in the diagonal directions, such as for the frequency ^^{e term} "^seP^ara^^^e" *^{s use<}^ ^{nere m} ^^ts

conventional sense, to mean a function of multiple coordinates that can be expressed as a product of separate functions of the individual coordinates, such as f(x,y) = g(x)h(y). The term "non-separable" is used in the present description and in the claims to refer to functions that cannot be separated in this manner.

Thus, for robust extended DOF, over a range of pupil shifts, phase plate 36 should have a cylindrically non-symmetrical and non-separable phase pattern. The phase plate is designed so that at each target spatial frequency /, the MTF defined by the above equation exceeds the threshold not only for a large range of defocuses z_a— z^, but also for a large range of possible shifts {sx, Sy and frequency vector directions a, wherein (f_x, fy) = f · (cosa, since). Solutions can be found by digital simulation and optimization of the above equation.

The optimization of phase plate 36, for example, can apply a general global optimization method, such as simulated annealing, to optimize a score function that evaluates the depth of focus of the system. The phase plate produces a through-focus MTF, which can be calculated as a function of the defocus parameter at several defocus points Δζ;

across the required depth of field. The target MTF value for a given frequency is MTFQ , with an allowed tolerance of

over the depth of field, i.e., the MTF value over this range should be between

On this basis, a score function for the through-focus MTF can be defined as:

wherein the summation is over all of the defocus parameter values within the desired depth of field. This score function optimizes the average performance of the phase plate.

The score function should also take into account various pupil-phase plate shifts and different MTF frequencies. The total score above can then be defined as a weighted average across these different shifts, frequencies, pupil sizes and any other relevant variables.

The optimization process takes as input a set of parameters for optimization and a model that translates these parameters into a sampled phase plate. The samples of the phase plate should be spaced closely enough to model the optical behavior of the phase plate correctly. For example, the phase plate may be modeled as a two-dimensional polynomial of a certain degree, and the corresponding parameters for optimization are the polynomial coefficients.

Alternatively, the optimization parameters may consist of a coarse grid of phase plate samples, wherein interpolation methods (such as spline interpolation) are used to determine the phase plate values between the given samples. This method requires only a relatively small number of parameters for optimization. The spacing of the coarse grid in this case is related to the MTF frequency that is observed. For example, the MTF at a frequency of / = 50 hp I mm is calculated by the autocorrelation of the phase plate at a distance of wherein

λ = 0.532μτη is the wavelength, and

is the focal length of the human eye. Therefore, choosing uncorrected phase plate values in a grid spaced 450 μιη or less apart will result in nearly zero MTF at 50 lp I mm. On the other hand, if the spacing of the coarse grid is too large, it limits the solution space unnecessarily. Therefore, the coarse grid spacing when evaluating the MTF at a certain frequency should typically be a little larger than the corresponding autocorrelation distance. For the example above of / = 50 Ip/mm, a spacing of 600 μιη gives good results.

Figs. 4A and 4B schematically illustrate a design of phase plate 36 that satisfies the above criteria, in accordance with an embodiment of the present invention. ). Fig. 4A is a graphical representation of the phase plate, in which the gray scale represents relative phase shift as a fraction of the design wavelength (λ). Fig. 4B is a numerical representation of these fractions, as computed by an optical design program given the constraints above. This figure contains a matrix 50 of numerical values, representing the phase shift at points that are spaced 0.6 mm apart. The overall, continuous phase profile of phase plate 36 can be calculated by spline interpolation between these point values.

The phase plate illustrated in Figs. 4A and 4B was optimized using the score function detailed above, for sixteen randomly-chosen pupil-phase plate shifts, based on the MTF calculated at a frequency of 50 bp I mm in four different directions (a = 0°, 45°, 90°, 135°). The required depth of field was 300 μιη (equivalent to ~1 diopter of visual accommodation), and the MTF value across the depth of field was required to be between MTF-L = 25% and MTF₂ = 45%. It can be seen both visually (in Fig. 4A) and mathematically (based on Fig. 4B) that the phase pattern of phase plate 36 is both cylindrically non- symmetrical and non-separable.

Although spline interpolation gives a continuous three-dimensional surface, for manufacturing purposes, this continuous surface can be quantized with negligible performance degradation. After quantization, the phase plate can be produced using etching techniques, or by suitable active devices, such as a spatial light modulator.

Fig. 5A presents plots 42 of MTF as a function of pupil shift for spectacles 26 containing the phase plate of Figs. 4A and 4B, in accordance with an embodiment of the present invention. These plots reflect optical MTF only, without the enhancement provided by image processor 30. The plots were calculated for sixteen different pupil shift vectors, chosen at random over a range of about ±2 mm along both x and y axes, and for four different MTF directions at each shift. The plots show that DOF enhancement is achieved for all shift vectors and MTF directions. In other words, phase plate 36 as shown above provides DOF enhancement that is robust against pupil shift.

Fig. 5B presents the best 70% of plots 42 from Fig. 5A. This figure illustrates that for most values of shift and MTF direction, the MTF is only slightly affected by defocus. Therefore, viewer 22 will generally see a sharp image over a substantial range of depths and pupil shifts.

Although the plots shown in Figs. 5 A and 5B were generated for certain specific random shifts, distributed approximately 0.5 mm apart, the expected performance of spectacles 26 for other shifts is similar, since phase plate 36 is designed to preserve the MTF value at a frequency of 50 lp/mm. Therefore, the phase plate is correlated at a distance of 450 μιη, and shifts smaller than this distance are not expected to change the performance significantly. DIGITAL ENHANCEMENT OF EXTENDED DOF

As noted earlier, image processor 30 applies digital filtering to pre-process stereographic images that are to be presented on screen 24. The digital filter kernel can be calculated as the inverse of the PSF of spectacles 26 (and specifically of phase plate 36). For example, in one embodiment, phase plate 36 applies aberrations that can be represented, for a pupil diameter of 5.6mm, in terms of the Zernike coefficients: Z4 = -0.85, Z9 = 0.4, Z16 = -0.2, and Z25 = -0.28; and the most significant part of the digital inverse-PSF filter has the following kernel:

Image processor 30 convolves each input image from content source 28 with the above kernel in order to generate the pre-processed image for display on screen 24.

As the digital convolution filter applied by image processor 30 is inverse to the mild blurring effect of the aberrations of phase plate 36, the convolution filter sharpens the digital image and may cause artifacts due to overshoot at high-contrast edges. In order to reduce these artifacts and provide a visually-pleasing image, while still enhancing DOF, image processor 30 may apply one or more of the following filtering operations to the image:

1. Clipping - After convolution, out-of-bounds pixel values (above the maximum or below the minimum permitted value) are clipped to the value of the nearest bound. Thus, for example, negative pixel values may be clipped to 0, while values above 255 are clipped to 255.

2. Reduce sharpening filter power - Modify the kernel values of the inverse-PSF filter in order to moderate the high-frequency response. Such a filter may produce weaker sharpening but will also produce fewer artifacts at high-contrast edges. 3. Scale dynamic range - In order to account for overshoot values and prevent or reduce clipping, the output pixel value range of the digital filter can be scaled down, so that the overshoots still fall within the permitted range (such as 0 to 255). In this approach, high- contrast edges may retain their original sharpness in the image seen by eye 32, at the expense of compressing the dynamic range of the pre-processed digital image relative to the original image.

4. Optimized optical design - The design of phase plate 36 may be modified so as to take into account the overshoot problem and minimize the overshoot insofar as possible. By directly optimizing the PSF and/or the image processing algorithm based on a score function that considers the overshoot ratio, the overshoot can be reduced.

5. Additional non-linear approaches - Image processor 30 may selectively apply different sharpening kernels depending on local contrast and/or pixel intensity, and/or may apply non-linear tone curve to the image pixels before or after the convolution.

Figs. 6A-6G show plots of the calculated step response of the eye at different virtual object distances, illustrating the effect of the elements of system 20 in accordance with an embodiment of the present invention. The virtual object distance (VOD) is the distance of a given object that is perceived by viewer 22 as a result of the stereographic display on screen 24 (due to vergence, as explained above, as opposed to the actual distance of the screen from the viewer). Each of Figs. 6A-6G represents the eye's response to a step image (in this case, a gray-level transition from 51 to 204, on a scale of 0-255) at the VOD value that is marked, in millimeters, above the figure. Thus, the VODs range from 1700 mm in Fig. 6A to, effectively, infinity in Fig. 6G. The plots assume that the accommodation of the eye follows vergence, so that the eye is focused at the VOD, as is the case for natural (not stereoscopic 3D) viewing conditions.

Each figure contains three plots:

• A baseline plot 54, showing the unaided response of eye 32.

• A focus-shifted plot 56, showing the response of eye 32 with the assistance of lens 38 to shift the eye's focus from 70 cm (the assumed distance to screen 24) to 4 m (closer to the vergence range).

• An enhanced DOF plot 58, showing the response of eye 32 with the assistance of both lens 38 and phase plate 36, following digital pre-processing of the step image by image processor 30. Phase plate 36 has the form defined by the Zernike coefficients: Z4 = -0.85, Z9 = 0.4, Z16 = -0.2, and Z25 = -0.28, as described above, while image processor 30 applies the digital filter represented by Table I, with clipping of overshoots.

With the eye accommodated at the 70 cm screen distance, plots 54 show that the image at the VOD is consistently blurred. This blurring is alleviated in part by the use of lens 38, as shown by plots 56, particularly at distances near the hyperfocal distance provided by the lens (Figs. 6D and 6E). Plots 58, however, show that with enhanced DOF, eye 32 sees a well-focused image at all VOD values, thus resolving the conflict of accommodation and vergence.

Figs. 7A-7C are simulated images comparing visual perception of image features in stereographic systems with and without DOF enhancement, in accordance with an embodiment of the present invention. These images were processed using the same set of assumptions as was used in generating the plots of Figs. 6A-6G. In each row, the base image (as shown in the upper-left box in Fig. 7A) is presented at a different VOD, as marked at the left side of the row. The left column ("No Optics") corresponds to plots 54, representing the unaided eye; the middle column ("Focus Shift") corresponds to plots 56, with the aid of lens 38; and the right column ("Enhanced DOF") corresponds to plots 58, with the assistance of digital preprocessing and phase plate 36. The benefit of the DOF enhancement provided by system 20 can be seen plainly in the clear images seen by the eye for VODs in the range from 1.7 m to infinity.

The figures above show that even with DOF enhancement, the effective PSF of images seen by eye 32 in system 20 still varies as a function of VOD. Thus, as an optional enhancement to the digital filtering functions described above, image processor 30 may modify the filter kernel that it applies to different images or to different parts of a single image based on variations in the VOD of objects in the images. For this purpose, the image processor uses VOD information with respect to objects in the images that is either provided as image metadata from content source 28 or is extracted by the image processor itself by comparing the object location in a stereographic image pair. For VOD values that are subject to more severe blurring (such as VOD below about 2 m in the example shown in Figs. 7A-7C), image processor 30 may then apply stronger sharpening. The strength of sharpening may thus vary from image frame to image frame, or even within a single image.

Another factor that can affect the PSF (or equivalently, the degree of image blur) is the distance of viewer 22 from screen 24. This distance (assumed in the above examples to be 70 cm) is used implicitly in determining the aberrations to be applied by phase plate 36 and the corresponding digital filtering properties to be applied by image processor 30. In an embodiment of the present invention, image processor 30 may use the distance between viewer 22 and screen 24 in optimizing the digital filtering kernel that it applies. The image processor may receive the appropriate distance value automatically from a depth sensor associated with the screen or manually as an input from the viewer.

Additionally or alternatively, the aberrations of phase plate 36 may be adjusted depending on the distance of the viewer from the screen. For example, two identical phase plates may be shifted relative to one another, whereby the degree of total aberration grows or shrinks depending on the relative alignment of the phase plates. Multiple viewers with spectacles of this sort can thus watch the screen together from different distances, and still enjoy the benefit of enhanced DOF. Further additionally or alternatively, adjustment of lenses 38 or a dynamic phase plate - base on a spatial light modulator, for example - may be used to compensate for different viewing distances.

Although the embodiments described above relate specifically to spectacles for stereographic viewing, in alternative embodiments (not shown in the figures), the principles of the present invention may similarly be applied in other sorts of stereographic systems, such as auto-stereoscopic (spectacle-free) displays and stereoscopic head-mounted displays (HMDs), in which the vergence-accommodation conflict occurs.

In a HMD, for example, each eye has an independent display adjacent to it. (Thus, typically, the HMD may actually comprise two separate display screens, but they are referred to simply as "a display" in the context of the present description and in the claims.) Collimating optics are coupled to the display to provide a sharp image of the display when the eye is focused to a distance much farther than the actual location of the display (typically in the range of 1 meter to infinity). This distance is defined as the collimation distance. Stereographic viewing can be achieved in a HMD by setting the viewing angle of the same object in the different displays to be the same as the viewing angle derived from the vergence of an object at a desired virtual distance. Since in HMD stereography, the collimating optics change the light wavefront in a way that mimics free propagation from the collimation distance, a virtual object that causes vergence to a distance that is different from the collimation distance will cause vergence-accommodation conflict.

This conflict can be resolved in the HMD by adding a phase plate for depth of field enhancement between the collimating optics and the eye. The phase plate is designed as in the embodiments described above, except that the display distance is taken to be the collimation distance. The phase plate in the HMD stereographic system will then have a similar effect on the depth of field as the phase plates described above for use in spectacles.

It will thus be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.

Claims

1. Apparatus for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the apparatus comprising:

spectacles comprising:

right and left optical filters, which are configured to be interposed respectively in front of the right and left eyes of the viewer so as to select the respective images for viewing by the right and left eyes; and

one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles; and a digital image processor, which is configured to pre-process the images presented on the stereographic display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

2. The apparatus according to claim 1, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

3. The apparatus according to claim 1, wherein the stereographic display is located at a given screen distance from the viewer and presents objects in the images at a virtual object distance, which is different from the screen distance, and wherein the one or more optical phase plates comprise a lens configured to compensate for a difference between the screen distance and the virtual object distance.

4. The apparatus according to claim 1, wherein the stereographic display is located at a given screen distance from the viewer, and wherein the one or more optical phase plates are adjustable responsively to the screen distance.

5. The apparatus according to any of claims 1-4, wherein the spectacles are configured to form images in the eyes with a point spread function (PSF) that is determined by the one or more optical phase plates, and wherein the digital filter is selected responsively to the PSF.

6. The apparatus according to claim 5, wherein the digital filter comprises a convolution kernel that is inverse to the PSF.

7. The apparatus according to claim 6, wherein application of the digital filter to the images causes overshoot artifacts at edges in the images, and wherein the digital image processor is configured to apply an additional operation to the filtered images so as to reduce the overshoot artifacts.

8. The apparatus according to any of claims 1-4, wherein the stereographic display is located at a given screen distance from the viewer, and wherein objects in the images presented on the stereographic display appear to the viewer to be located at respective virtual object distances, which are different from the screen distance, and wherein the digital image processor is configured to vary the digital filter responsively to variations in the virtual object distances of the objects appearing in different images.

9. The apparatus according to any of claims 1-4, wherein the one or more optical phase plates have a predefined, cylindrically non- symmetrical and non-separable phase pattern.

10. Spectacles for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the spectacles comprising:

one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined, cylindrically non-symmetrical and non-separable phase pattern selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles.

11. The spectacles according to claim 10, wherein the stereographic display is located at a given screen distance from the viewer and presents objects in the images at a virtual object distance, which is different from the screen distance, and wherein the one or more optical phase plates comprise a lens configured to compensate for a difference between the screen distance and the virtual object distance.

12. The spectacles according to claim 10, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

13. The spectacles according to any of claims 10-12, wherein the cylindrically nonsymmetrical and non-separable phase pattern is selected so that the depth of field is enhanced over a range of shifts of pupils of the eyes relative to the spectacles.

14. Spectacles for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the spectacles comprising:

one or more optical phase plates, which are positioned adjacent to the right and left filters and are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

15. A method for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the method comprising:

providing spectacles to be worn by the viewer, the spectacles comprising:

one or more optical phase plates, which are positioned adjacent to the right and left filters and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles; and pre-processing the images presented on the stereographic display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

16. The method according to claim 15, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, and wherein providing the spectacles comprises selecting the aberrations so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

17. The method according to claim 15, wherein the stereographic display is located at a given screen distance from the viewer and presents objects in the images at a virtual object distance, which is different from the screen distance, and wherein the one or more optical phase plates comprise a lens configured to compensate for a difference between the screen distance and the virtual object distance.

18. The method according to claim 15, wherein the stereographic display is located at a given screen distance from the viewer, and wherein providing the spectacles comprises adjusting the one or more optical phase plates responsively to the screen distance.

19. The method according to any of claims 15-18, wherein the spectacles are configured to form images in the eyes with a point spread function (PSF) that is determined by the one or more optical phase plates, and wherein pre-processing the images comprises selecting the digital filter responsively to the PSF.

20. The method according to claim 19, wherein the digital filter comprises a convolution kernel that is inverse to the PSF.

21. The method according to claim 20, wherein application of the digital filter to the images causes overshoot artifacts at edges in the images, and wherein pre-processing the images comprises applying an additional operation to the filtered images so as to reduce the overshoot artifacts.

22. The method according to any of claims 15-18, wherein the stereographic display is located at a given screen distance from the viewer, and wherein objects in the images presented on the stereographic display appear to the viewer to be located at respective virtual object distances, which are different from the screen distance, and wherein pre-processing the images comprises varying the digital filter responsively to variations in the virtual object distances of the objects appearing in different images.

23. The method according to any of claims 15-18, wherein the one or more optical phase plates have a predefined, cylindrically non- symmetrical and non-separable phase pattern.

24. A method for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the method comprising:

interposing right and left optical filters respectively in front of the right and left eyes of the viewer so as to select the respective images for viewing by the right and left eyes; and

positioning, adjacent to the right and left filters, one or more optical phase plates having a predefined, cylindrically non-symmetrical and non-separable phase pattern selected so as to enhance a depth of field of the eyes while the eyes view the stereographic display through the spectacles.

25. The method according to claim 24, wherein the stereographic display is located at a given screen distance from the viewer and presents objects in the images at a virtual object distance, which is different from the screen distance, and wherein positioning the one or more optical phase plates comprises providing a lens to compensate for a difference between the screen distance and the virtual object distance.

26. The method according to claim 24, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, wherein the method comprises selecting the aberrations so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

27. The method according to any of claims 24-26, wherein positioning the one or more optical phase plates comprises selecting the cylindrically non- symmetrical and non-separable phase pattern so that the depth of field is enhanced over a range of shifts of pupils of the eyes relative to the spectacles.

28. The method according to claim 27, wherein selecting the cylindrically non-symmetrical and non-separable phase pattern comprises optimizing the phase pattern so that a modulation transfer function (MTF) of the eyes engendered by the one or more optical phase plate is within a desired MTF range over a specified depth of field for multiple, different shifts of the pupils.

29. A method for viewing a stereographic display, which presents different, respective images for viewing by a right eye and a left eye of a viewer, the method comprising:

positioning, adjacent to the right and left filters, one or more optical phase plates that are configured to introduce aberrations in the images seen by the right and left eyes, wherein the method comprises selecting the aberrations so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

30. Apparatus for stereographic imaging, comprising:

a display, which is configured to present different, respective images for viewing by a right eye and a left eye of a viewer; and

one or more optical phase plates, which are positioned in an optical path between the display and the right and left eyes and have a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the display.

31. The apparatus according to claim 30, and comprising a digital image processor, which is configured to pre-process the images presented on the display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

32. The apparatus according to claim 30, and comprising right and left optical filters, which are configured to be interposed respectively in front of the right and left eyes of the viewer so as to select the respective images for viewing by the right and left eyes.

33. The apparatus according to claim 30, wherein the display and the one or more optical phase plates are configured to be mounted on a head of the viewer.

34. The apparatus according to any of claims 30-33, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

35. The apparatus according to any of claims 30-33, wherein the one or more optical phase plates have a predefined, cylindrically non- symmetrical and non-separable phase pattern.

36. A method for stereographic imaging, comprising:

presenting on a display different, respective images for viewing by a right eye and a left eye of a viewer; and

positioning one or more optical phase plates in an optical path between the display and the right and left eyes, the one or more optical phase plates having a predefined aberration selected so as to enhance a depth of field of the eyes while the eyes view the display.

37. The method according to claim 36, and comprising pre-processing the images presented on the display by applying a digital filter selected so as to compensate for the aberration of the optical phase plates.

38. The method according to claim 36, and comprising interposing right and left optical filters, respectively, in front of the right and left eyes of the viewer so as to select the respective images for viewing by the right and left eyes.

39. The method according to claim 36, and comprising mounting the display and the one or more optical phase plates on a head of the viewer.

40. The method according to any of claims 36-39, wherein the one or more optical phase plates are configured to introduce aberrations in the images seen by the right and left eyes, and wherein the aberrations are selected so as to reduce a variation of a point spread function (PSF) of the eyes with object distance.

41. The method according to any of claims 36-39, wherein the one or more optical phase plates have a predefined, cylindrically non- symmetrical and non-separable phase pattern.