Design Of Computer-generated Holograms Research Articles

Design framework of a computer-generated hologram that performs volumetric beam shaping for advanced laser processing

Axial beam shaping is very effective for material laser processing, typically laser cutting, drilling, and grooving. We demonstrate a framework for designing a computer-generated hologram (CGH) that performs volumetric beam shaping. The procedure performs axial beam shaping with a continuous intensity distribution, unlike our previous research in which only discrete focal points were arranged three-dimensionally. This research is the more general approach for volumetric beam shaping. An important point in this research is finding an optimal interval in the optical axis direction and in calculating the CGH design. The design interval is half of the focusing length (the full width at half-maximum of the laser beam profile in the axial direction) given by the diffraction limit of the optical system. The optimal value is obtained using an axially shaped beam that is the reconstruction of the CGH calculated from Zernike polynomials. We also demonstrate that the optimal interval for evaluating the axially shaped beam is also half of the beam length. Following the CGH design procedure, we demonstrate CGHs that generate long-focus beams with an arbitrary axially shaped beam. We found a tradeoff relation between the focusing length and the intensity of the long-focus beam, suggesting that the use of a focused beam with an appropriate length according to the purpose will lead to improved processing efficiency.

Substrate calibration method of a computer-generated hologram based on ray propagation in a three-dimensional model.

In interferometry with a computer-generated hologram (CGH), the substrate error of the CGH limits its high-precision aspheric measurement application. The propagation form of the substrate error is still ambiguous although 0th-order calibration can partly correct it. We established the ray propagation in a three-dimensional model in order to solve the ambiguity of substrate error propagation. This method shows the modulation process of the CGH substrate error on the transmitted wavefront for the first time, until now, to the best of our knowledge. The experiments show that the propagation of the substrate error can be accurately analyzed, and the CGH design efficiency also is significantly improved after applying this method.

Band-amplified angle spectrum method for the phase hologram design to achieve high-quality holographic imaging in long distance

The angular spectrum method (ASM) is widely used in the design of computer-generated holograms (CGH) due to its strict adherence to the Helmholtz equations and the potential for accelerated computation using fast Fourier transform (FFT). However, when dealing with long distance propagation conditions, the reduction of effective spectral components and spectral aliasing will introduce significant computation errors, leading to a substantial degradation in holographic imaging quality. To achieve high-quality holographic imaging design in long distance, we introduce a novel angular spectrum computation method, the calculation process is divided into two steps: (1) First propagate a longer distance from the CGH plane to an intermediate plane. (2) Then continue to propagate to the observation plane after incorporating a spread spectrum phase factor to amplify the effective non-aliased bandwidth in the intermediate plane and eliminating the aliasing artifacts. Furthermore, the non-uniform fast Fourier transform (NUFFT) algorithm is adopted which allows for the flexible adjustments of the sampling interval and quantity in the spatial frequency domain, all while maintaining compliance with the Nyquist sampling theorem even in the context of bandwidth amplification. Both simulations and optical experiments are conducted to validate the feasibility and effectiveness of our proposed method.

Design of computer-generated holograms based on semi-rigorous simulations of sub-wavelength structures.

Conventional design methods for computer-generated holograms often rely on the scalar diffraction theory because the calculation effort of rigorous simulations is too high. But for sub-wavelength lateral feature sizes or large deflection angles, the performance of realized elements will show distinct deviations from the expected scalar behavior. We propose a new design method that overcomes this issue by incorporating high-speed semi-rigorous simulation techniques that allow the modeling of light propagation at an accuracy close to the rigorous methods. This includes an approach to solve the inverse problem of calculating a geometric structure that is able to form a certain physical field distribution.

Solving optimal carrier frequencies of a CGH null compensator through a double-constrained searching method based on iterative ray-tracings.

Interferometry based on a computer-generated hologram (CGH) null compensator is a general method for high-precision metrology of aspherics. Because the most commonly used CGHs are the Ronchi type with only two quantization steps, tilt and defocus carrier frequencies must always be introduced to separate the disturbing diffraction orders (DDOs). Determining the amount of carrier frequencies is a pivotal but difficult issue in the CGH design process. Previous studies have only drawn qualitative conclusions or obtained some approximate results under specific conditions. This paper proposes a double-constrained searching method based on iterative ray-tracings, which can directly and accurately give the optimal combination of tilt and defocus carrier frequencies, as long as the aspheric under test is a concave one and has an analytical expression. The optimal carrier frequencies solved by the proposed method will minimize the line density of the CGH on the premise of separating all DDOs, which will reduce the cost and difficulty of fabrication as much as possible. The proposed method is almost error-free and holds a clear advantage over the previous methods in terms of versatility. Several typical design examples are presented to verify the feasibility and versatility of the proposed method. Its accuracy is also verified through making comparisons of the ray-tracing results between another method and Zemax models based on these examples.

Asymmetric Optical Wavelength Switch Based on LCoS-SLM for Edge Node of Optical Access Network

A novel design of optical wavelength switch, based on an asymmetric switching architecture for edge node implementation, is presented in this paper. Compared to previous research for optical core transport network applications, the proposed work has a unique aspect to build dynamic multicasting and spectral equalization, vital functionalities for optical wavelength switch in the edge of optical access networks. An optical wavelength switch was experimentally implemented and evaluated in a 4 × 16 switching architecture to demonstrate the concept. This dynamic multicasting and spectral equalization were achieved by utilizing liquid crystal on a silicon spatial light modulator (LCoS-SLM) device. An optimal design of computer-generated holograms (CGHs) through an improved GS algorithm was used to perform the beam steering and wavelength switching. A variety of wavelength switching scenarios has been experimentally evaluated. The measurement results showed an average insertion loss of around -12.5 dB, and the calculated crosstalks were all less than -28 dB. Its applications in digital data transmissions were evaluated to achieve a transmission speed larger than 2.5 Gbps. The eye diagram measurement results showed that most wavelength switching scenarios have nearly bit-error-free transmission. The scenario includes the multicasting with spectral equalization within the proposed asymmetrical switching architecture.

Multiplexed recording based on the reference wave correlation for computer-generated holographic data storage

Holographic data storage (HDS) based on a computer-generated hologram (CGH) technique has been proposed as a promising approach to realize an in-line and simple HDS system. This work focuses on multiplexed recording for CGH-based HDS, and the approach based on the reference wave correlation is introduced to the HDS. For the proposed method, the processes for a CGH design are modified to generate reference waves with different phase distributions for each recording. Since holograms are recorded to the same region in a medium with independent reference waves, recorded data-pages are selectively reconstructed by the corresponding reference wave illuminations. The experimental demonstration confirms the feasibility of the proposed method, and the theoretical characteristic for the number of recordable multiplexed holograms is estimated by the numerical simulation.

Machine learning based technique towards smart laser fabrication of CGH

Fabrication of Computer-Generated Holograms (CGHs) on metal surfaces is a challenging procedure, given the nature of the laser-matter interaction specified for metals, and the power requirements for silver laser machining. A machine learning approach is derived for engraving of CGHs on silver surfaces with a 1070 nm fiber laser. The proposed method paves the way towards an automated solution for the fabrication of CGH on silver surfaces that accounts for, in terms of manufacturability. Sophisticated image-based descriptors are extracted from digital holographic masks produced by commercial CGH design software to predict, using machine learning, a “quality score” from ‘1’ to ‘5’, estimating the fabrication feasibility of a CGH's mask. Based on this idea, the procedure of CGH engraving on silver is remarkably improved.

Single-shot phase retrieval with complex diversity.

The concept of complex diversity is introduced that adequately accounts for special considerations in the design of the system and the reconstruction algorithm for single-shot phase retrieval techniques. Complex-number pupil filters containing both amplitude and phase values are extracted by numerical propagation from a computer-generated hologram design, which generates multiple images in a single acquisition. The reconstruction is performed by a Fourier iterative algorithm modified with an area restriction to avoid noise amplification. Numerical simulations show that the complex diversity technique estimates extrinsic Kolmogorov aberration better than conventional single-shot techniques for a distant point object. Experiments show that sensorless adaptive optics correction is achieved using the complex diversity technique.

用于高精度非球面面形检测的计算全息图的设计

用于高精度非球面面形检测的计算全息图的设计

Optimal design of tilt carrier frequency computer-generated holograms to measure aspherics.

Computer-generated holograms (CGHs) provide an approach to high-precision metrology of aspherics. A CGH is designed under the trade-off among size, mapping distortion, and line spacing. This paper describes an optimal design method based on the parametric model for tilt carrier frequency CGHs placed outside the interferometer focus points. Under the condition of retaining an admissible size and a tolerable mapping distortion, the optimal design method has two advantages: (1)separating the parasitic diffraction orders to improve the contrast of the interferograms and (2)achieving the largest line spacing to minimize sensitivity to fabrication errors. This optimal design method is applicable to common concave aspherical surfaces and illustrated with CGH design examples.

Spiral phase plates with radial discontinuities for the generation of multiring orbital angular momentum beams: fabrication, characterization, and application

A design of spiral phase plates for the generation of multiring beams carrying orbital angular momentum (OAM) is presented. Besides the usual helical profile, these phase plates present radial π-discontinuities in correspondence of the zeros of the associated Laguerre polynomials. Samples were fabricated by electron beam lithography over glass substrates coated with a polymethylmethacrylate resist layer. The optical response was analyzed and the purity of the generated beams was investigated in terms of Laguerre-Gaussian modes contributions. The far-field intensity pattern was compared with theoretical models and numerical simulations, while the expected phase features were confirmed by interferometric analysis with a Mach-Zehnder setup. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order OAM beams with nonzero radial index. An application consisting of the design of computer-generated holograms encoding information for light beams carrying phase singularities is presented and described. A numerical code based on an iterative Fourier transform algorithm has been developed for the computation of phase-only diffractive optical element for illumination under OAM beams. Numerical analysis and preliminary experimental results confirm the applicability of these devices as high-security optical elements for anticounterfeiting applications.

Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

Computer-generated holograms (CGHs) are commonly used to test aspheric surfaces. In order to eliminate the influence of spurious diffraction orders, adequate carrier frequency is applied to CGHs to separate the overlapping orders. This paper describes a paraxial parametric model for separating the parasitic diffraction orders of a tilt carrier frequency CGH placed outside the interferometer focus. The approximate analytical expression for the disturbing field on the filter plane is derived using the paraxial model. This expression provides a recipe for determining the amount of tilt carrier frequency needed to eliminate the disturbing orders, and is applicable to concave weak aspheric surfaces with large f-numbers of the best-fit spheres, where paraxial approximation is valid. CGH design examples are provided.

Design of dense transmission diffraction gratings for high efficiency.

We propose a design method for dense surface-relief diffraction gratings with high efficiency in transmission mode. Closed-form analytical relations between diffraction efficiency, polarization, and grating parameters are derived and verified in the resonance domain of diffraction under general three-dimensional angles of incidence traditionally termed conical mounting. A powerful tool for rigorous design of computer-generated holograms and diffractive optical elements with spectroscopic scale periods is now enabled.

Spatial bandwidth analysis of fast backward Fresnel diffraction for precise computer-generated hologram design.

Designing near-field computer-generated holograms (CGHs) for a spatial light modulator (SLM) requires backward diffraction calculations. However, direct implementation of the discrete computational model of the Fresnel diffraction integral often produces inaccurate reconstruction. Finite sizes of the SLM and the target image, as well as aliasing, are major sources of error. Here we present a new design prescription for precise near-field CGHs based on comprehensive analysis of the spatial bandwidth. We demonstrate that, by controlling two free variables related to the target image, the designed hologram is free from aliasing and can have minimum error. To achieve this, we analyze the geometry of the target image, hologram, and Fourier transform plane of the target image to derive conditions for minimizing reconstruction error due to truncation of spatial frequencies lying outside of the hologram. The design prescription is verified by examples showing reconstruction error versus controlled parameters. Finally, it is applied to precise three-dimensional image reconstruction.

Design and analysis of an alignment procedure using computer-generated holograms

A procedure that uses computer-generated holograms (CGHs) to align an optical system’s meters in length with low uncertainty and real-time feedback is presented. The CGHs create simultaneous three-dimensional optical references, which are decoupled from the surfaces of the optics allowing efficient and accurate alignment even for systems that are not well corrected. The CGHs are Fresnel zone plates, where the zero-order reflection sets tilt and the first-diffracted order sets centration. The flexibility of the CGH design can be used to accommodate a wide variety of optical systems and to maximize the sensitivity to misalignments. An error analysis is performed to identify the main sources of uncertainty in the alignment of the CGHs and to calculate the magnitudes in terms of general parameters, so that the total uncertainty for any specific system may be estimated. A system consisting of two CGHs spaced 1 m apart is aligned multiple times and re-measured with an independent test to quantify the alignment uncertainty of the procedure. The calculated and measured alignment uncertainties are consistent with less than 3 μrad of tilt uncertainty and 1.5 μm of centration uncertainty (1σ ).

Asphericity and Discrete Phase Calculation for Optical Freeform Surface Test with Computer Generated Holograms

Optical freeform surfaces are complex surfaces with non-rotational symmetry that break through the limitations of conventional optical element, and are widely used in advanced optics application for system configuration simplifying and performance enhancing. Interferometric test with computer generated holograms (CGH) has been widely used in the aspherical surfaces testing for their unique wavefront transformation, as well as the freeform surfaces testing with high precision. As an important parameter, it is different at the definition of asphericity in freeform surfaces manufacture and test. Asphericity for interferometric test which verifies the testing ability of the CGH and determines testing system initial configuration was calculated with minimum maximum angle deviation. Reverse ray tracing could get the optimal solution of CGH local phase at certain location in the CGH design. For the non-rotational symmetry of freeform surfaces, the phase of sample point in CGH surface should be calculated in three-dimensional coordinate system. The calculation method of discrete phase was deduced by ray tracing, as well as the phase distribution on freeform surface were proven by calculating in such way. The results were compared with simulation by optical design software. It shows that the method is right and high accuracy to be used in the CGH design for the freeform surfaces.

Spherical aberrations and manufacturing errors in eliminating the substrate errors of a computer-generated hologram (withdrawn)

This paper [Opt. Eng. 52(9), 091723 (2013)] was removed from the SPIE Digital Library on 24 July 2013 by the publisher upon verifying that a significant portion of Section 4 of the paper was taken directly from the following previously published paper without attribution: Ping Zhou and James H. Burge, “Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors,” Optics Express 15(23), 15410 (2007). The citation is provided here so that interested readers can access the information from the original source.

Comparison of different simulation methods for effective medium computer generated holograms

The arrangement of binary subwavelength structures is a promising alternative to the conventional multiheight level technique to generate computer generated holograms (CGHs). However, the current heuristic design approach leads to a slight mismatch between the target signal and experimental data. To evaluate this deviation, a diffractive beam splitter design is investigated rigorously using a finite-difference time-domain (FDTD) method. Since the use of a rigorous Maxwell-equation solver like FDTD requires a massive computational effort, an alternative scalar approach, a fast Fourier transform beam propagation method (FFT-BPM), is investigated with a substantial higher computing speed, showing still a good agreement with the FDTD simulation and experimental data. Therefore, an implementation of this scalar approach into the CGH design process offers the possibility to significantly increase the accuracy.

Suppression of the zero-order diffracted beam from a pixelated spatial light modulator by phase compression

Phase compression is used to suppress the on-axis zero-order diffracted (ZOD) beam from a pixelated phase-only spatial light modulator (SLM) by a simple modification to the computer generated hologram (CGH) loaded onto the SLM. After CGH design, the phase of each SLM element is identically compressed by multiplying by a constant scale factor and rotated on the complex unit-circle to produce a cancellation beam that destructively interferes with the ZOD beam. Experiments achieved a factor of 3 reduction of the ZOD beam using two different liquid-crystal SLMs. Numerical simulation analyzed the reconstructed image quality and diffraction efficiency versus degree of phase compression and showed that phase compression resulted in little image degradation or power loss.