Problems on design of computer-generated holograms for testing aspheric surfaces: principle and calculation

Interferometric optical testing using computer-generated hologram (CGH) has provided an approach to highly accurate measurement of aspheric surfaces. While designing the CGH null correctors, we should make them with as small aperture and low spatial frequency as possible, and with no zero slope of phase except at center, for the sake of insuring lowisk of substrate figure error and feasibility of fabrication. On the basis of classic optics, a set of equations for calculating the phase function of CGH are obtained. These equations lead us to find the dependence of the aperture and spatial frequency on the axial diszance from the tested aspheric surface for the CGH. We also simulatethe ptical path difference error of the CGH relative to the accuracy of controlling laser spot during fabrication. Meanwhile, we discuss the constraints used to avoid zero slope of phase except at center and give a design result of the CGH for the tested aspheric surface. The results ensure the feasibility of designing a useful CGH to test aspheric urface fundamentally.     

Design and fabrication of computer-generated holograms for testing optical freeform surfaces

Freeform optical surfaces (FOSs) will be the best elements in the design of compact optical systems in the future. However, it is extremely difficult to measure freeform surface with sufficient accuracy, which impedes the development of the freeform surface. The design and fabrication of computer-generated hologram (CGH) , which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F-θ lens. A new eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the new procedure meets the requirements.     

波带板法检测非球面技术

总结了在波带板干涉技术检测非球面方面最近的发展和应用，比较了不同方法的优缺点。叙述了用一块改进型波带板检测非球面的原理和方法。还分析了波带板的安装与测量精度的关系。针对干涉条纹在周边弯曲的现象，对波带板的设计进行了改进。最后给出了实验结果。     

On-axis computer-generated holograms for three-dimensional display

The feasibility of on-axis synthetic near-field amplitude holograms for three-dimensional display applications is demonstrated. An iterative optimization algorithm is used that generates an object-dependent diffuser that utilizes the phase and, to some extent, amplitude freedoms in the reconstruction plane. The discrimination between twin images and undiffracted terms is thus improved. The on-axis approach presents important advantages: a low coherence requirement for the illuminating source, a lower spacebandwidth and higher viewing angle than with the off-axis alternatives. Defocusing and parallax are experimentally attained with an extended white-light source and a lensless setup.     

Comparison of in-line and carrier frequency holograms in aspheric testing

We show the possibility and the conditions of the filtering of in-line holograms in aspheric testing. A general comparison of in-line and carrier frequency holograms applied to aspheric testing is also given.     

Analytical study of disturbing diffraction orders in in-line computer generated holograms for aspheric testing

The effect of spurious diffraction orders due to an in-line diffractive compensator for the measurement of aspheric surfaces is analytically studied. The use of a filtering aperture to isolate the measurement diffraction order from the stray orders introduces additional spurious fields that must be analyzed for a correct evaluation of surface defects. In this work the influence of the additional diffraction orders is studied and an analytical expression for the disturbing field on the detector is obtained.     

Wavefront-linearization in construction of computer-generated holograms

The application of computer-generated holograms for 3-D information handling requires reconstructions of image details at finite distances from the hologram plane. To calculate the hologram structure Huygens' principle may be used. To treat this problem in an alternative mathematical way a linearization was introduced. The effects of such a procedure are evaluated and illustrated with analytical and optical reconstructions.     

The use of commercial fine-grain films for computer-generated holograms

The possible use of commercial fine-grain films for computer-generated binary holograms is described. Three different types of film are used. Image quality improves with film resolution but if the resolving power is higher than a minimum value needed for the phase level resolution, the contrast (γ value) of the film has a pronounced effect on the quality of the image reconstructed optically from the hologram. The possible generation of binary holograms by computers with reduced central memory is also studied.     

Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

A new theta modulation multiplexing scheme for computer-generated holograms

In this paper, a new theta modulation multiplexing scheme for producing multiplexed computer-generated holograms (CGHs) is proposed. Under this scheme, normal Lohmann-type CGHs are individually modulated by gratings with different orientations and then superimposed to form a single hologram. The proposed method results in a higher storage capacity without the increase of hologram space. Theoretical analysis and experimental results are presented.     

Phase coding in iterative synthesis of computer-generated holograms

A new method is investigated for phase-only hologram synthesis. The method combines iterative calculation of the hologram phase function with the coding of the amplitude-phase characteristics of the complex transmission function into phase characteristics. The results of computational experiments are presented. The phase masks and reconstructed object images are also presented.     

Optical particle trapping with computer-generated holograms written on a liquid-crystal display

Computer-generated holograms written on a liquid-crystal display can be used to generate dynamic light fields of arbitrary shape. This method was used to simultaneously trap polystyrene particles laterally and to displace them independently of one another.     

Measurement accuracy verification of aspheric surface test with computer-generated hologram

A convex aspheric surface using a computer-generated hologram(CGH) test plate fabricated with novel techniques and equipment is tested.However,the measurement result is not verified via comparison with other methods.To verify the accuracy of the measurement,a perfect sphere surface is measured by the following.The measurement result is quantified into four parts:the figure error from the tested spherical surface;the figure error from the reference spherical surface;the error from the hologram;and the adjustment error from misalignment.The measurement result,removed from the later three errors,shows agreement to 4-nm RMS with the test by Zygo interfermeter of the same surface.Analysis of the CGH test showed the overall accuracy of the 4-nm RMS,with 3.9 nm from the test plate figure,0.5 nm from the hologram,and 0.74 nm from other sources,such as random vibration,various second order effects,and so on.Thus,the measurement accuracy using the proposed CGH could be very high.CGH can therefore be used to measure aspheric surfaces accurately.     

Optimization of computer-generated holograms for dynamic optical manipulation with uniform structured light spots

An optimized iterative technique combining the merits of conventional Gerchber-Saxton (G-S) and adaptive-additive (A-A) algorithms to design multilevel computer-generated holograms for the creation of a desirable structured intensity pattern for multiple optical manipulation is theoretically adopted. Optical trap arrays are demonstrated with the help of liquid crystal spatial light modulator and a microscopic optical tweezer system. Additionally, continuous locked-in transport and deflection of microparticles with the generated optical lattice is proven experimentally. The proposed method possesses apparent high efficiency, high uniformity, and dynamic and reconfigurable advantages.     

Diffraction-limited laser beam shaping by use of computer-generated holograms with dislocations

A new method that reshapes a Gaussian laser beam into a polygon of diffraction-limited size with a flat or a pyramidal top is presented. The technique is based on the use of computer-generated holograms with phase dislocations (singularities).     

利用环形子孔径拼接法检测非球面反射镜

为解决高精度检测非球面反射镜的难题,提出利用Zygo干涉仪完成非球面环形子孔径检测。通过移动待测非球面,使得由干涉仪产生的参考球面波,以不同的曲率半径匹配待测非球面的各个环带区域,分别测试每个环带,进而完成对整个非球面的拼接检测。以双曲面反射镜为例进行拼接检测,并搭建辅助光路,利用无像差点法对拼接结果进行验证。验证结果表明:该方法测量误差小于1/20 （=632.8 nm）。     

Optical reconstruction of 3D images by use of pure-phase computer-generated holograms

A three-dimensional （3D） object reconstruction technique that uses pure-phase computer-generated holograms （CGHs） and a phase-only spatial light modulator （SLM） is proposed. The full parallax CGHs are generated by the point source method and the wave-oriented method without paraxial approximation. Different from conventional CGHs, the pure-phase information on the hologram plane is loaded on the SLM to reconstruct the 3D diffusive objects without considering the reference wave. This technique is more efficient in its utilization of the space-bandwidth product of the SLMs. Numerical simulations and experiments are performed, and the results show that our proposed method can reconstruct 3D diffusive objects successfully.     

Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography

We have developed a new multiplexing method for producing binary computer-generated holograms (CGH's) for security applications. This method is based on double recording of two types of coding method upon binary CGH's. The CGH synthesized by the proposed method can have multiple image planes from the region close to the hologram (image region) to infinity (Fraunhofer region) without severe degradation of reconstructed images in the image region. A CGH containing simultaneous image- and Fourier-type holograms is fabricated by electron-beam lithography. Some experimental results are presented.     

一种薄非球面透镜的加工与检测

介绍了外径为 φ14 8mm、厚度为 5mm的月牙形非球面透镜加工的一些工艺难点及解决方法 ,并给出了检验方案。对加工过程中出现的变形原因及克服方法进行了探讨 ,并给出了透镜最终的检测结果。     

Flexible interferometry for optical aspheric and free form surfaces

Optical Review - A flexible interferometry is proposed to test concave optical aspheric and free-form surfaces. It employs a flexible aberration generator (FAG) consisting of a movable reflective...