Radiation imagery chemistry: process – composition – or product th – Including control feature responsive to a test or measurement
Reexamination Certificate
1999-04-26
2001-06-19
Nguyen, Nam (Department: 1756)
Radiation imagery chemistry: process, composition, or product th
Including control feature responsive to a test or measurement
C430S321000, C359S565000, C359S569000, C359S571000, C359S575000
Reexamination Certificate
active
06248487
ABSTRACT:
STATEMENT OF GOVERNMENT INTEREST
The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon.
BACKGROUND OF THE INVENTION
This invention relates to diffractive optical elements, and more particularly to a method to synthesize amplitude and phase weights for desired diffractive patterns for optical elements in applications using phase-only spatial light modulators (SLM) and diffractive optical elements, their mathematical design, physical realization and fabrication procedure.
Phase errors can profoundly distort the intended diffraction patterns of spatial light modulators (SLMs) thus impacting the performance of optical processing systems that use SLMs. Phase errors are introduced by a variety of mechanisms. Phase-modulating SLMs can have inherent phase errors, due to fabrication process variations from pixel to pixel. Noise (e.g. thermal, quantization, etc.) on the video signals modulating SLMs is also transformed into phase errors. Furthermore, many applications, including composite filters for pattern recognition, binary diffractive optics and optical neural networks, can often be better understood and analyzed by modeling the modulations/signals as random, rather than as deterministic. This viewpoint has led to the invention/development of statistically based methods of design and new devices that arise from these design methods. This is the subject of this invention.
Random phase modulations across the surface of the SLM diffract into broadly spread noise patterns. These noise patterns not only have the appearance of speckle patterns, but in fact, arise from the identical situation of scattering of light from a random surface. There is a wealth of information on laser speckle (J. C. Dainty,
Laser Speckle and Related Phenomena
, Springer, 1984) and statistical optics (J. W. Goodman,
Statistical Optics
, Wiley, 1985) that is applicable to SLM-based optical processors. This invention was motivated by the opinion that speckle theory could be applied to advance the performance of optical processors that use SLMs and to lead to new applications of SLMs. More specifically, the present invention is an improvement on the technology of the following U.S. patents, the disclosures of which are incorporated herein by reference: U.S. Pat. No. 4,588,260 issued to Horner;
U.S. Pat. No. 4,765,714 issued to Homer;
U.S. Pat. No. 5,363,186 issued to Cohn and Liang; and
U.S. Pat. No. 5,276,636 issued to Cohn.
Both of the Cohn and Homer patents deal with SLM technology, and Cohn uses pseudorandom encoding of SLM systems. Improvements in diffraction efficiency, uniformity and signal-to-noise ratios is possible with the improvements to pseudorandom encoding (including partial encoding) of spatial light modulators that are described in this invention.
Traditional theories of speckle generation by rough surface scattering are adapted to analyzing SLMs. SLMs are modeled as arrays of sub apertures/pixels that are perturbed by random phase components. While traditional speckle theory models random surfaces as stationary random processes, SLMs can be programmed to produce nonstationary optical surfaces. This generalization is used to devise a new class of computer generated holography algorithms, referred to as pseudorandom encoding. The method is notable in that it 1) uses all available space bandwidth of the SLM; 2) produces diffraction patterns having large signal to noise ratio; and, most notably, 3) can be calculated in real-time by serial processors.
SUMMARY OF THE INVENTION
The invention includes several improvements to the method described in U.S. Pat. No. 5,363,186. One improvement includes the use of phase-only pseudorandom encoding in which improvements in diffraction efficiency, uniformity and signal-to-noise ratios are possible with the partial encoding aspects of speckle generation by phase-only spatial light modulators.
One embodiment of the present invention is a process to synthesize the desired diffraction by selecting appropriate values of the phase of a far field pattern of a phase-only spatial light modulator and which follow from using the principles of speckle generation. Speckle patterns are produced by scattering plane waves off of rough surfaces and observing the resulting pattern of intensity at some distance from the surface. This process begins by selecting the desired far field pattern of the diffractive optical wave emitted by the spatial light modulator. The next step entails performing a fast Fourier transform on the desired far field pattern of the diffractive optical wave to get a desired source distribution description for the diffractive optical wave. Next, pixel amplitudes a
i
are set for each pixel i: and pixel phases are set by a combination of random phase selection for specified portions of the diffraction pattern, and conventional pixel phase selection methods, such as the MEDOF method discussed below.
Other embodiments of the invention entail a variation on this process that uses partial pseudorandom encoding with coupled amplitude phase spatial light modulators, in which the pixel amplitude is expressed as a function of phase; or modulators that can produce any value of phase and binary values of amplitude, where the pixel amplitude has a value of 1 or 0, and is chosen pseudorandomly using binary statistics.
The individual improvements include the use of a search for fully complex functions that when pseudorandom encoded produce improved diffraction patterns having higher diffraction efficiency and lower noise. The search selects random phases for specified positions across the diffraction pattern. The search can be done without using fast Fourier transforms and thus it has a low numerical overhead. The method is especially useful for spot array generators and composite filters for pattern recognition. For spatially continuous diffraction patterns the arbitrarily random phases are known to produce nonuniformities across the diffraction pattern referred to as speckle. Specific diffusers have been developed in the field of holography to minimize this speckle effect. The speckle in this invention differs from holography applications in that the speckle is designed to appear in regions of the diffraction pattern where no, or minimal optical energy is desired.
The present invention is also a method referred to as partial pseudorandom encoding. It enhances the diffraction efficiency and uniformity, and reduces the noise level of diffraction patterns by encoding some of the desired fully complex values by the pseudorandom encoding method and encoding the remainder by using a method referred to as MEDOF. (MEDOF is described in R. D. Juday, Optimal realizable filters and the minimum Euclidean distance principle, Applied Optics, 32(26),5100-5111. (1993), the disclosure of which is incorporated herein by reference.) In MEDOF the points on the operating curve of the SLM that are closest to the desired (but unimplementable) complex values are used in place of the desired complex values. In MEDOF, there is also a search based on varying a threshold radius and (for non-circular SLM operating curves) angle that leads to the best performance. In partial pseudorandom encoding there is also a search over radius and angle that optimizes performance. There is a distinction between the MEDOF search and the partial. encoding search in that for some modulators (most notably the phase-only modulator) there is no improvement possible by using MEDOF, but there is improvement by using partial encoding.
The present invention is also a method for performing pseudorandom encoding of coupled amplitude-phase SLMs. This is to say the amplitude can be expressed as a function of phase. The method is a type of histogram equalization that makes the coupled amplitude-phase encoding process look like phase-only pseudorandom encoding. Two specific embodiments of the design method, one for a linear coupling of amplitude to phase and another for arbitrary coupling but using binary phase statistics are p
Bidiwala Shaad
Cohn Robert W.
Auton William G.
Nguyen Nam
The United States of America as represented by the Secretary of
Ver Steeg Steven A.
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