BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1-8 depict exemplary embodiments of the present invention.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
FIG. 1 shows the principle of a suitable technique on a simple image according to the present invention. Due to the limited size of the arrays, the boarder of the output image is not a real interference as only one phase image is present. Thus the output image does not carry information, but the N−1 by N−1 core of the output represents the binary data according to equation (2).
Any digital data page can be coded into a phase image according to the following simple recursive formula shown in equation (3) based on an inversion of equation (1):
E
i+1,j+1
in
=E
i,j
out
−E
i,j (3)
If a Di,j binary data page (consisting of elements of 0 and 1) is needed to be generated at the output (the intensity is Ii,jout=I0·Di,j where I0 is a constant intensity), the recursive formula for the binary input phase page (consisting of elements of 0 and π phases) is:
Φi+1,j+1=(Φi,j/π+Di,j−1)
The image duplication and shift can be implemented by different optical solutions like a birefringent plate (as shown in FIG. 2). If the birefringence axis is not parallel to the propagation direction of the incident beam, the propagation direction of the ordinary and the extraordinary polarization components is typically different, and thus the extraordinary component is laterally shifted after traversing the plate. In this way, two phase images with orthogonal polarization are present after being subjected to the birefringent plate. For making them interfere, a polarizer with polarization a axis angular to both the ordinary and the extraordinary polarization direction can be introduced. The interference pattern then can be captured by a CCD camera, for example. (See i.e. the optical systems of FIG. 3 and 4.)
The birefringent plate introduces constant phase shifts to the images, which can be different for the ordinary and the extraordinary images. The difference between the phase shifts can be adjusted by slightly turning the plate from perpendicular incidence. If the phase difference is 0 or an integral multiple of 2π, the above equations are valid. If the phase shifts are opposite i.e. the difference is π or an odd multiple of π, the interference of the points with the same initial phases is dark, and the interference of points with initially different phases is bright. This adjustment is advantageous, for example because a high contrast output image can be achieved even if the phase levels of the input images are not perfectly 0 and π.
FIG. 1 demonstrates how a phase coded image is decoded to an intensity image. FIG. 1a) shows the complex amplitude of the phase coded image (containing values of 1 and −1 corresponding to phases of 0 and π), its spatially shifted replica and the coherent sum of them. FIG. 1b) shows the absolute value square of the amplitudes of FIG. 1a) presenting the corresponding intensities. The first image table presents the intensity of the phase coded image, which is constant, the second is its spatially shifted replica, and the third is the intensity distribution of their interference. The inner part of the resultant image contains intensities of 0 and 4 providing the decoded binary image.
FIG. 2 shows how a birefringent plate (1) can duplicate and shift an image by double refraction. In case of normal incidence, the ordinary polarization component (4) of the incident beam (3) traverses the plate without refraction, and the extraordinary one (5) is refracted at the incidence plane, propagates angularly in the plate, and exits from the plate in a parallel direction, but shifted to the ordinary one. Also shown in FIG. 1 is the optical axis (2) of the birefringent plate.
FIG. 3 shows an embodiment of the decoding optical system using a birefringent plate for image duplication and shift in case of a transparent phase object. The encoded phase image can be generated with a phase modulating spatial light modulator (7) illuminated with a polarized plane wave (7). The imaging optics (8) projects the image of the phase object to the detector plane (12), and the image duplication and shift is made just before this plane (12). The birefringent plate (10) splits and shifts the extraordinary polarization from the ordinary one as shown in FIG. 2. The ratio of the intensities in the two beams is adjusted with the half-wave plate (9), and the polarizer (11) polarizes the two beams to the same direction in order to make them interfere, giving a decoded intensity pattern.
FIG. 4 shows an embodiment of the decoding optical system using a birefringent plate for image duplication and shift in the case of a reflective phase object. The encoded phase image can be generated with a reflective phase modulating spatial light modulator (14) illuminated with plane wave (13) polarized by a polarizing beam splitter (20) which transmits the orthogonal polarization reflected from the phase modulating spatial light modulator (14) which may include, for example, a wave retarder to adjust the proper polarization. The imaging, shifting and capturing part is generally the same as in FIG. 3. The imaging optics (15) project the image of the phase object to the detector plane (19), and the image duplication and shift is made just before this plane (19). The birefringent plate (17) splits and shifts the extraordinary polarization from the ordinary one as shown, for example, in FIG. 2. The ratio of the intensities in the two beams is adjusted with the half-wave plate (16), and the polarizer (18) polarizes the two beams to the same direction in order to make them interfere, giving the decoded intensity pattern.
FIG. 5 shows an embodiment of the decoding optical system using a plan-parallel plate with a partly reflecting mirror and a totally reflecting mirror for image duplication and shift. The encoded phase image carried by the laser beam (21) is imaged on the detector plane (24), and the image duplication and shift is made just before this plane (24). One portion of the beam is reflected on a front mirror (22) which is partly reflecting; the other part is reflected on a rear mirror (23) which is totally reflecting. The two beams interfere at the camera plane, giving a decoded intensity pattern.
FIG. 6 shows an embodiment of the decoding optical system obtained by splitting the light beam and introducing angular shift between the beams at the Fourier plane of the phase image by a small angle prism with a partly and a totally reflective surface. The phase image (25) is generally at the front focal plane of the Fourier transforming lens (26), and at the back focal plane of the lens, a partly reflective mirror (27) reflects one part of the beam carrying the Fourier transform of the phase image, and the other part is reflected on a totally reflective mirror (28) in an angularly shifted direction. The second Fourier transforming lens (29) gives the image plane (30) in its back focal plane, where the angular shift in the Fourier plane is transformed into spatial shift, and the two shifted images interfere in order to produce the intensity pattern.
FIG. 7 shows an embodiment of the decoding optical system obtained by splitting the light beam and introducing angular shift between the beams at the Fourier plane of the phase image by a diffracting or by a Wollaston prism. The phase image (31) is at the front focal plane of the Fourier transforming lens (32), and at the back focal plane of the lens, a diffraction grating or a Wollaston prism (33) splits the beam carrying the Fourier transform of the phase image, and introduces angular shift between the two beams. The second Fourier transforming lens (34) gives the image plane (35) in its back focal plane, where the angular shift in the Fourier plane is transformed into spatial shift, and the two shifted images interfere to produce the intensity pattern. If a Wollaston prism is used to split the beam into two with orthogonal polarization, a polarizer can advantageously be placed at the image plane with intermediate direction to make them interfere.
FIG. 8 shows an embodiment of the decoding optical system obtained by splitting the light beam and introducing angular shift between the beams at the Fourier plane of the phase image by a polarization beam splitter prism and two mirrors. The phase image (36) is at the front focal plane of the Fourier transforming lens (37), and at the back focal plane of the lens (that is, the Fourier transform of the phase image), the beam is split into two and an angular shift is introduced between the two beams with the following advantageous setup. A polarization beam splitter prism (39) splits the beam; the intensity ratio of the transmitted and the reflected beams is set by a half-wave plate (38). Both the transmitted and the reflected beams are reflected back by a quarter-wave plate (40) and a mirror (41) at both sides of the prism, and then they come out from the prism with a small angle shift between them that is up to 5-10° or less. The two beams are of orthogonal polarization so a polarizer (42) with intermediate axis makes them able to interfere. The second Fourier transforming lens (43) gives the image plane (44) in its back focal plane, where the angular shift in the Fourier plane is transformed into spatial shift, and the two shifted images interfere to produce the intensity pattern.
Additional advantages, features and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, and representative devices, shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.
All documents referred to herein are specifically incorporated herein by reference in their entireties.
The use of singular article terms including “an”, “a” and “the” can connote the singular or plural of the object that follows.
Patent Application
20080002897
