Reflection volume holographic scanners with field-curvature corrections

A new type of polygonal holographic scanner that combines a reflection volume hologram with a computer-generated hologram (CGH) is described. The scanner is free from the aberration of field curvature. Such a scanning system can allow for a compact folded version of the scanner and Bragg diffraction into only a single order. The equations expressing the spatial-variable image distance are derived and are fit to the phase function designated by polynomials incorporated into a CGH in terms of the least-squares method. A reflection scanner with field-curvature correction is made by interfering a diffracted wave front from this CGH with a spherical wave front having scanning focal power through a second plane hologram. Experiments demonstrating the feasibility of this scanner are presented. Raster-scan patterns using a multifaceted scanner are shown. Helpful data on the diffraction efficiency and the spectrally diffracted intensity of reflection holograms are also presented.     

Efficient testing of segmented aspherical mirrors by use of reference plate and computer-generated holograms. I. Theory and system optimization

Telescopes with large aspherical primary mirrors collect more light and are therefore sought after by astronomers. Instead of large mirrors as a single piece, they can be made by use of numerous smaller segments. Because the segments must fit together to create the effect of a single mirror, segmented optics present unique challenges to fabrication and testing that are absent for monolithic optics. We have developed a new method for measuring large quantities of segments accurately, quickly, and economically using an interferometric test plate and computer-generated hologram (CGH). In this test, the aspheric mirror segments are interferometrically measured by use of a test plate with a best-fit spherical surface. The aspherical departure is accommodated with a small CGH that is imaged onto the test plates. The radius of curvature is tightly controlled by maintaining the gap between the test plate and the segment. We present a summary of the test and give the basic design tradeoffs for using a single system to measure all of the segments of a large aspheric mirror.     

Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel-Fourier CGH, the Fresnel CGH, and the image CGH. These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.     

Spherical beam volume holograms for spectroscopic applications: modeling and implementation

The spherical beam volume hologram, recorded by a plane wave and a spherical beam, is investigated for spectroscopic applications in detail. It is shown that both the diffracted and the transmitted beam can be used for spectroscopy when the hologram is read with a collimated beam. A new method is introduced and used for analysis of the spherical beam volume hologram that can be extended for analysis of arbitrary holograms. Experimental results are consistent with the theoretical study. It is shown that the spherical beam volume hologram can be used in a compact spectroscopic configuration when the transmitted beam is monitored. Also, on the basis of the properties of the spherical beam hologram, the response of a hologram recorded by a plane wave and an arbitrary pattern is predicted. The information can be used to optimize holographic spectrometer design.     

Dual Computer-generated Holograms for Testing Aspherical Surfaces

The use of a dual computer-generated hologram for performing interferometric testing of aspherical surfaces is described. The dual hologram consists of apertures whose positions are modulated along two different directions. The dual hologram allows the simultaneous generation of two different wavefronts whose sum and difference can be obtained with appropriate spatial filtering. This has been proved theoretically and verified experimentally. Finally, the dual hologram is utilized to test steep aspherics, and some practical advances of the dual hologram are mentioned.     

Design of transmission-type phase holograms for a compact radar-cross-section measurement range at 650 GHz

A design formalism is presented for transmission-type phase holograms for use in a submillimeter-wave compact radar-cross-section (RCS) measurement range. The design method is based on rigorous electromagnetic grating theory combined with conventional hologram synthesis. Hologram structures consisting of a curved groove pattern on a 320 mmx280 mm Teflon plate are designed to transform an incoming spherical wave at 650 GHz into an output wave generating a 100 mm diameter planar field region (quiet zone) at a distance of 1 m. The reconstructed quiet-zone field is evaluated by a numerical simulation method. The uniformity of the quiet-zone field is further improved by reoptimizing the goal field. Measurement results are given for a test hologram fabricated on Teflon.     

凹非球面检测的双计算全息图设计及制作

基于全息补偿检验非球面的原理,提出并设计了一种二元纯相位型双计算全息图.该全息图由主全息和对准全息两部分组成,用于检测非球面的主全息位于基底的中心,而对准全息位于其边缘,用来精确定位主全息,从而消除离焦、偏心及倾斜所引入的误差.两部分全息同心是实现对主全息准确定位的前提,为此,提出了"一次曝光,两次刻蚀"的制作方法,即一次性将两部分图形在同一块掩膜版上制作出,曝光一次后,基底经两次刻蚀制作出具有两种不同相位深度的双计算全息图.最后给出了一个检测?40、F2抛物面镜的双计算全息设计实例,并将其检测结果与自准直检测结果比较,二者吻合良好,验证了该设计方法的正确性及制作工艺的可行性.     

Reconfigurable optical interconnects by a combined computer-generated hologram and spatial light modulator method

A new method for implementing electrically addressed dynamic optical interconnects is presented. In this approach a phase spatial light modulator (SLM) is combined with a computer-generated hologram (CGH). The phase SLM is used to change the phase of the wave front that illuminates the CGH. Binary orthogonal phase codes are used to address the SLM. The CGH is designed with iterative discrete on-axis encoding so that different wave fronts direct light to different locations. High efficiency can be achieved because of the large number and the small dimensions of pixels in the CGH. The dynamic aspects result from the use of an SLM that may have a relatively small number of relatively large pixels. In this manner a high-efficiency programmable interconnect system with fast reconfiguration time based on current technology devices may be implemented. The CGH-SLM method yields connection efficiencies significantly higher than previous methods that are based on the use of thin optical elements. Simulation results indicate that for switch sizes in the range from 1 × 2 to 1 × 8, connection efficiencies of higher than 1/ √N (where N is the number of possible destinations) are feasible.     

Embedding of computer-generated hologram in a dithered image

We have developed an encryption method using a computer-generated hologram (CGH) embedded in a dithered image. First, confidential information is converted into a CGH. Next, the CGH data undergo two separate dithering processes in parallel: one corresponding to CGH white pixels and one corresponding to CGH black pixels. The results from both processes are used to form a dither matrix for creating the final dithered and encoded image. In this way, confidential information can be embedded into the image. The confidential information can be extracted using a technique similar to CGH optical reconstruction.     

Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates

A method other than the extended-boundary-condition method (EBCM) to compute the T matrix for electromagnetic scattering is presented. The separation-of-variables method (SVM) is used to solve the electromagnetic scattering problem for a spheroidal particle and to derive its T matrix in spheroidal coordinates. A transformation is developed for transforming the T matrix in spheroidal coordinates into the corresponding T matrix in spherical coordinates. The T matrix so obtained can be used for analytical calculation of the optical properties of ensembles of randomly oriented spheroids of arbitrary shape by use of an existing method to average over orientational angles. The optical properties obtained with the SVM and the EBCM are compared for different test cases. For mildly aspherical particles the two methods yield indistinguishable results. Small differences appear for highly aspherical particles. The new approach can be used to compute optical properties for arbitrary values of the aspect ratio. To test the accuracy of the expansion coefficients of the spheroidal functions for arbitrary arguments, a new testing method based on the completeness relation of the spheroidal functions is developed.     

Null test for a highly paraboloidal mirror

A circular null computer-generated hologram (CGH) was used to test a highly paraboloidal mirror (diameter, 90 mm; f number, 0.76). To verify the null CGH test a classic autocollimation test with a flat mirror was performed. Comparing the results, we show that the results of the null CGH test show good agreement with results of the autocollimation test.     

Axial tolerance in the position of aberration compensators placed in a converging beam

To perform a null test of aspherical surfaces we used a computer-generated hologram or a lens or a mirror compensator to compensate the aspherical aberration. When compensating in a convergent light beam the axial position of this hologram or compensator is critical. A holographic compensator to be used in the convergent beam of light was designed and constructed. We have established some relations to determine the tolerance in the axial positioning of these compensators.     

Effective reduction of the novel look-up table memory size based on a relationship between the pixel pitch and reconstruction distance of a computer-generated hologram

In this paper, we propose an approach, new to our knowledge, to effectively generate and reconstruct the resolution-enhanced computer-generated hologram (CGH) of three-dimensional (3-D) objects with a significantly reduced in memory size novel look-up table (N-LUT) by taking into account a relationship between the pixel pitch and reconstruction distance of the hologram pattern. In the proposed method, a CGH pattern composed of shifted versions of the principal fringe patterns (PFPs) with a short pixel pitch can be reconstructed just by using the CGH generated with a much longer pixel pitch by controlling the hologram reconstruction distance. Accordingly, the corresponding N-LUT memory size required for resolution-enhanced hologram patterns can be significantly reduced in the proposed method. To confirm the feasibility of the proposed method, experiments are carried out and the results are discussed.     

Precise focal-length measurement technique with a reflective Fresnel-zone hologram

A new technique for precise focal-length measurement with a hologram is presented. This technique is widely applicable and is particularly useful for measuring large, slow lenses. In diffraction, the Fresnel-zone plate hologram emulates the reflective properties of a convex spherical mirror for use during transmission null tests of an optic by use of a phase-shifting interferometer. The hologram is written lithographically and therefore offers a higher degree of precision at a lower cost than its spherical mirror counterpart. A hologram offers the additional benefit of easy characterization by use of the same interferometer employed in examining the test optic. Better than +/-0.01% precision is achieved during measurement of a 9-m focal-length lens by use of a 150-mm aperture interferometer.     

Fast computation for generating CGH of a 3D object by employing connections between layers

An approximate method for generating computer-generated holograms (CGH) of a 3D object with six times faster speed than the conventional algorithm is presented. In the conventional algorithm, a 3D object is sliced into many layers and treated as a collection of self-illuminated point light source. The propagation process of a light ray from every point of an object to all the points on the hologram plane is simulated and interfered with by the reference beam to form a CGH. In our proposed method, under the assumption that the depth of a 3D object is much smaller than the recording distance, we just need to calculate the oblique distance between the first layer and the hologram plane, and then the oblique distances from the other layers to the hologram plane can be obtained from a simple relation, thus the computational time is much reduced. The CGH is optically reconstructed and the quality of the reconstructed image agrees well with that from the conventional algorithm.     

Decomposition storage of information based on computer-generated hologram interference and its application in optical image encryption

An information-encryption method based on computer-generated hologram (CGH) interference is presented. In this method the original information is decomposed into two parts, and then each part is encoded on a separate CGH. When these two encoded CGHs are aligned and illuminated, a combined interference pattern is formed. The original information is obtained from this pattern. It is impossible to decrypt the original information from one CGH alone; two matched CGHs must be put together to make it available.     

Interferometric testing for off-axis aspherical mirrors with computer-generated holograms

The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the nonzero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer.     

Testing the effect of computer-generated hologram fabrication error in a cylindrical interferometry system

This paper presents a method of testing the effect of computer-generated hologram (CGH) fabrication error in a cylindrical interferometry system. An experimental system is developed for calibrating the effect of this error. In the calibrating system, a mirror with high surface accuracy is placed at the focal axis of the cylindrical wave. After transmitting through the CGH, the reflected cylindrical wave can be transformed into a plane wave again, and then the plane wave interferes with the reference plane wave. Finally, the double-pass transmitted wavefront of the CGH, representing the effect of the CGH fabrication error in the experimental system, is obtained by analyzing the interferogram. The mathematical model of misalignment aberration removal in the calibration system is described, and the feasibility is demonstrated via the simulation system established in Zemax. With the mathematical polynomial, most of the possible misalignment errors can be estimated with the least-squares fitting algorithm, and then the double-pass transmitted wavefront of the CGH can be obtained by subtracting the misalignment errors from the result extracted from the real experimental system. Compared to the standard double-pass transmitted wavefront given by Diffraction International Ltd., which manufactured the CGH used in the experimental system, the result is desirable. We conclude that the proposed method is effective in calibrating the effect of the CGH error in the cylindrical interferometry system for the measurement of cylindricity error.     

阶梯形浮雕和折射率位相光栅的衍射性质比较

位相全息图一般既有浮雕调制又有折射率调制,它们都会对衍射特性产生影响。利用以严格电磁波理论为基础的模式匹配法（ＭＭＴ）,从理论上比较了阶梯形浮雕位相调制光栅和折射率位相调制光栅对ＴＥ波的各级衍射效率。尽管它们同一周期内的相应部分所引起的位相变化相同,但随着光栅层厚度的加大两种位相调制光栅的各级衍射效率会出现差别。这种差别与周期有关。并将矢量理论的结果与标量理论的结果进行了比较,研究结果对研究全息术