Wavefront Coding Research Articles

Broadband photon sieves imaging with wavefront coding.

A novel method for broadband imaging of using a diffractive photon sieves is proposed and experimentally demonstrated. Unlike conventional photon sieves imaging in which clear imaging is only valid at a single designed wavelength due to the strong wavelength-dependent nature of diffractive elements, broadband photon sieves imaging is implemented with wavefront coding of a simple cubic phase mask without complicated optical system to compensate large chromatic aberration. Experimental validation was performed using an UV-lithography fabricated photon sieves of a focal length of 500mm and a diameter of 50mm at designed wavelength 632.8nm and a diamond-turning fabricated cubic phase mask of a phase parameter α=20π. Results show that extension of the working bandwidth of the proposed photon sieves imaging system is at least 88 times that of a conventional one with almost the same optical resolution and much increased energy efficiency. The proposed method suggests a new concept of extending the applications of photon sieves to work in a broadband wavelength range with a simple method in contrast to conventionally work at a single wavelength only.

Imaging and image restoration of an on-axis three-mirror Cassegrain system with wavefront coding technology.

Wavefront coding (WFC) technology is adopted in the space optical system to resolve the problem of defocus caused by temperature difference or vibration of satellite motion. According to the theory of WFC, we calculate and optimize the phase mask parameter of the cubic phase mask plate, which is used in an on-axis three-mirror Cassegrain (TMC) telescope system. The simulation analysis and the experimental results indicate that the defocused modulation transfer function curves and the corresponding blurred images have a perfect consistency in the range of 10 times the depth of focus (DOF) of the original TMC system. After digital image processing by a Wiener filter, the spatial resolution of the restored images is up to 57.14 line pairs/mm. The results demonstrate that the WFC technology in the TMC system has superior performance in extending the DOF and less sensitivity to defocus, which has great value in resolving the problem of defocus in the space optical system.

Aperture shape dependencies in extended depth of focus for imaging camera by wavefront coding

Optical transfer functions (OTFs) on various directional spatial frequency axes for cubic phase mask (CPM) with circular and square apertures are investigated. Although OTF has no zero points, it has a very close value to zero for a circular aperture at low frequencies on diagonal axis, which results in degradation of restored images. The reason for close-to-zero value in OTF is also analyzed in connection with point spread function profiles using Fourier slice theorem. To avoid close-to-zero condition, square aperture with CPM is indispensable in WFC. We optimized cubic coefficient α of CPM and coefficients of digital filter, and succeeded to get excellent de-blurred images at large depth of field.

Combined analysis of tunable phase mask within spatial and frequency domain

Wavefront coding technique is a powerful technique which overcomes the defects of traditional way to extend depth of field. By inserting a phase mask into the traditional incoherent imaging system, wavefront coding technique does not reduce the resolution and the light gathering power of the optical system but enlarges the depth of field of incoherent imaging system. Although several kinds of phase masks have been reported, cubic phase mask is still of a classical type which has been investigated widely both in spatial and frequency domain. Since the phase profiles of phase masks adopted in classical wavefront coding systems are predefined with specific optical systems, the extension of depth of field is not tunable. Tunable wavefront coding systems are introduced by using a pair of detachable phase masks, which is possible to control the depth of field and bandwidth of system by changing the position of each component with respect to the pupil center. Ojeda-Castaeda [Ojeda-Castaeda J, Rodrguez M, Naranjo R 2010 Proceedings of Progress in Electronics Research Symposium, Cambridge, July 58, 2010 p531] proposed to use a pair of cosine phase masks to make defocus sensitivity tunable. Zhao [Zhao H, Wei J X 2014 Opt. Commun. 326 35] investigated an improved version of Ojeda- Castaneda's design in frequency domain and found that the proposed system realized tunable bandwidth. The present study, based on the work of Zhao, analyzes the tunable characteristics of a pair of simple modified detachable cubic phase masks in spatial domain and frequency domain. Firstly, the ray aberration theory is adopted to give mathematical analyses and ray aberration maps of the proposed tunable phase mask. Based on the mathematical derivations, the size of point spread function (PSF) of system can be changed not only by profile of each cubic mask but also by the each mask displacement relative to pupil center. Secondly, a mathematical PSF based on the stationary phase method is derived in spatial domain. Simulations indicate that the positions of PSF translate in the image plane with the displacements of phase mask profile and the position of each component with respect to the pupil center. By analyzing the oscillations of PSF, the effective bandwidth is obtained. Through the expression, we can conclude that the effective bandwidth can be changed by the position, mask profile of each component and defocus. Only when the addition of two mask profiles is large enough, can the effective bandwidth be simplified without adding the influence of defocus. In addition, though the approximate expression of magnitude transfer of function (MTF) has been given by adopting stationary phase method in the appendix of previous work, it cannot give an intuitive grasp of the effective bandwidth in MTF map. Unlike the MTF expression derived before, the exact optical transfer function (OTF) expression is derived by adopting Fresnel integral in frequency domain. Exact MTF and phase transfer function (PTF) can be derived from OTF. Based on the exact MTF expression, simulations give an intuitive effective bandwidth in MTF map. Simulations also show the nonlinear property of PTF. The effective bandwidth and MTF can be changed by different phase mask profiles and positions, which indicate that the effective bandwidth and defocus sensitivity can be tuned. Analyses are conducted both in spatial domain and in frequency domain to verify the tunable property of the proposed phase mask, which provides theoretical foundation for tunable wavefront coding system design.

コマ収差による3次位相変化を用いたWavefront CodingにおけるPSF補正に基づく復元画像の画質改善

本論文では，像面上でのPSFの空間的な変化に着目し，復元に用いるPSFを実際のPSFとの差分が小さくなるように変化させることにより，広い被写界深度を保ちつつ，WFC復元画像の画質改善を実現することを目的とする．単一PSFを拡大縮小回転で変形させた複数のPSFを用いて画像を復元すること，像面でのPSF変化が小さくなるように撮像面を傾斜させることの二つの手法を提案する．シミュレーションと実際の撮像レンズによる実験を行い，被写体距離を変えた場合のWFC復元画像の解像度に関して定量的な評価を行った．その結果，復元画像の画質を改善でき，提案手法の有効性を確認できた．

相位板偏心对波前编码系统的成像影响分析

相位板偏心对波前编码系统的成像影响分析

波前正交编码阵列被动测距系统

波前正交编码阵列被动测距系统

Cramer-Rao bounds in functional form: theory and application to passive optical ranging.

A functional approach to the multivariate statistical model of a generalized incoherent passive optical ranging and imaging system with a CCD sensor is proposed. This approach implies that a large number of discrete, statistically independent, random data (pixel readouts) can be approximated by a continuous random function. Thus, the joint probability density function (PDF) takes a functional form; the statistical averages of the infinite-variate PDF and the Fisher information become functional integrals that can be treated analytically in the Gaussian approximation. The Cramer-Rao bounds on estimator-error variances are obtained for the scalar and functional deterministic parameters of the model. An approximate expression is derived for the PDF of the sum of independent Gaussian and Poisson random variables using the steepest-descent method, and the resulting PDF is shown to be asymptotically Gaussian. As an illustration, we apply the developed approach to a passive optical rangefinder with chiral wavefront coding. Numerical and experimental examples are presented.

Enhancing the performance of the light field microscope using wavefront coding.

Light field microscopy has been proposed as a new high-speed volumetric computational imaging method that enables reconstruction of 3-D volumes from captured projections of the 4-D light field. Recently, a detailed physical optics model of the light field microscope has been derived, which led to the development of a deconvolution algorithm that reconstructs 3-D volumes with high spatial resolution. However, the spatial resolution of the reconstructions has been shown to be non-uniform across depth, with some z planes showing high resolution and others, particularly at the center of the imaged volume, showing very low resolution. In this paper, we enhance the performance of the light field microscope using wavefront coding techniques. By including phase masks in the optical path of the microscope we are able to address this non-uniform resolution limitation. We have also found that superior control over the performance of the light field microscope can be achieved by using two phase masks rather than one, placed at the objective's back focal plane and at the microscope's native image plane. We present an extended optical model for our wavefront coded light field microscope and develop a performance metric based on Fisher information, which we use to choose adequate phase masks parameters. We validate our approach using both simulated data and experimental resolution measurements of a USAF 1951 resolution target; and demonstrate the utility for biological applications with in vivo volumetric calcium imaging of larval zebrafish brain.

Wavefront-coding technique for inexpensive and robust retinal imaging.

We propose a hybrid optical-digital imaging system that can provide high-resolution retinal images without wavefront sensing or correction of the spatial and dynamic variations of eye aberrations. A methodology based on wavefront coding is implemented in a fundus camera in order to obtain a high-quality image of retinal detail. Wavefront-coded systems rely simply on the use of a cubic-phase plate in the pupil of the optical system. The phase element is intended to blur images in such a way that invariance to optical aberrations is achieved. The blur is then removed by image postprocessing. Thus, the system can provide high-resolution retinal images, avoiding all the optics needed to sense and correct ocular aberration, i.e., wavefront sensors and deformable mirrors.

Optimized asymmetrical tangent phase mask to obtain defocus invariant modulation transfer function in incoherent imaging systems

Wavefront coding as an optical-digital hybrid imaging technique can be used to extend the depth of field. The key to wavefront coding lies in the design of suitable phase masks to achieve the invariant imaging properties over a wide range of defocus. In this Letter, we propose another phase mask with a tangent function to enrich the odd symmetrical kind of phase masks. The performance of the tangent phase mask is evaluated by comparison with a cubic mask, improved-1 logarithmic mask, improved-2 logarithmic mask, and sinusoidal mask. The results demonstrate that the tangent phase mask has superior performance in extending the depth of field.

The alignment and imaging experiment of a telescope with wavefront coding technology

Wavefront coding (WFC) is kind of computational imaging technique that controls misfocus and misfocus-related aberrations of optical systems by appending a specially designed phase distribution to the pupil function. This technology has been applied in many fields to increase the performance or/and reduce the cost of imaging systems. The application of WFC technology on an off-axis three-mirror anastigmatic (TMA) system has been proposed in our previous work. In this letter, we describe the alignment, the imaging experiment and image restoration of an actual TMA system with WFC technology. 2014 中文 Optics Letters.

Simulation analysis of the depth of field characteristic of negative refraction flat lens

In virtue of wave-front coding theory, a computer simulation analysis of the depth of field extension of negative refraction flat lens is carried out. The depth of field extension can be achieved by 6.7 times in the slab, when its index is -1, through computer simulation. When the refractive index of the tablet is slightly offset, taking -0.99 for example, 6.9 times of the depth of field extension can be achieved after the introduction of the calibration lens.

基于传统显微系统的波前编码显微系统设计研究

基于传统显微系统的波前编码显微系统设计研究

Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging

Imaging three-dimensional structures represents a major challenge for conventional microscopies. Here we describe a Spatial Light Modulator (SLM) microscope that can simultaneously address and image multiple targets in three dimensions. A wavefront coding element and computational image processing enables extended depth-of-field imaging. High-resolution, multi-site three-dimensional targeting and sensing is demonstrated in both transparent and scattering media over a depth range of 300-1,000 microns.

Hyper Gaussian windows with fractional wavefronts

For reducing the impact of focus errors on the modulation transfer function (MTF), we explore the use of fractional phase power masks combined with either sub Gaussian windows, or super Gaussian windows. We present a sub Gaussian mask combined, with an asymmetric fractional phase profile, which reduces both the variations of the MTF vs. focus errors and the oscillations of the MTF around its tendency curve. However, this mask also reduces the light throughput by a factor of two. Full Text: PDF References M. Mino, Y. Okano, "Improvement in the OTF of a Defocused Optical System Through the Use of Shaded Apertures", Appl. Opt. 10, 2219-2225 (1971). CrossRef J. Ojeda-Castaneda, L. R. Berriel Valdos and E. L. Montes, "Line-spread function relatively insensitive to defocus", Opt. Lett. 8, 458-460 (1983). CrossRef J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, "Ambiguity function as a design tool for high focal depth", Appl. Opt. 27, 790-795, (1988). CrossRef E. R. Dowski, T. W. Cathey, "Extended depth of field through wave-front coding", Appl. Opt. 34, 1859-1865 (1995). CrossRef N. George, W. Chi, "Extended depth of field using a logarithmic asphere", J. Opt. A - Pure Appl. Opt. 5, 157-163 (2003). CrossRef A. Sauceda and J. Ojeda-Castaneda, "High focal depth with fractional-power wave fronts", Opt. Lett. 29, 560-562 (2004). CrossRef A. Castro and J. Ojeda-Castaneda, "Asymmetric Phase Masks for Extended Depth of Field", Appl. Opt. 43, 3474-3479 (2004). CrossRef S. Mezouari, G. Muyo, A. R. Harvey, "Circularly symmetric phase filters for control of primary third-order aberrations: coma and astigmatism", J. Opt. Soc. Am. A 23, 1058-1062 (2006). CrossRef J. Ares García, S. Bará, M. Gomez García, Z. Jaroszewicz, A. Kolodziejczyk, and K. Petelczyc, "Imaging with extended focal depth by means of the refractive light sword optical element", Opt. Exp. 16, 18371 (2008). CrossRef J. Ojeda-Castaneda, J. E. A. Landgrave and C. M. Gómez-Sarabia, "Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field", Appl. Opt. 47, E99 ? E105 (2008). CrossRef J. Ojeda-Casta-eda and Arturo Noyola-Isgleas, "High focal depth by apodization and digital restoration", Appl. Opt. 27, 2583-2586 (1988). CrossRef W. T. Cathey and E. R. Dowski, "New Paradigm for Imaging Systems", Appl. Opt. 41, 6080-6092 (2002). CrossRef J. Ojeda-Castaneda, E. Yépez-Vidal, E. García-Almanza and C. M. Gómez-Sarabia, "Tunable Gaussian mask for extending the depth of field", Photonics Letters of Poland, Vol. 4 (3), 115-117 (2012). DirectLink N. Brenner and C. Rader, "A new principle for fast Fourier transformation", IEEE Acoustics, Speech & Signal Processing 24, 264?266 (1976). CrossRef

Stationary phase analysis of generalized cubic phase mask wavefront coding

The modified generalized cubic phase mask (GCPM) has recently been applied in wavefront coding systems including infrared imaging and microscopy. In this paper, the stationary phase method is employed to analyze the GCPM characteristics. The SPA of the modulation transfer function (MTF) under misfocus aberration is derived for a wavefront coding system with a GCPM. The approximation corresponds with the Fast Fourier Transform (FFT) approach. On the basis of this approximation, we compare the characteristics of GCPM and cubic phase masks (CPM). A GCPM design approach based on stationary phase approximation is presented which helps to determine the initial parameter of phase mask, significantly decreasing the computational time required for numerical simulation.

Introduction to Wavefront Coding for Incoherent Imaging

We propose in this paper an introduction to the wavefront coding technique for incoherent imaging. Wavefront coding introduces image processing in the conception of an imaging system. It consists in introducing controlled aberrations in the optics able to reduce, after processing, some defaults of the optical system such as defocus, chromaticity. We present the basis of wavefront coding and illustrate them on two images with different characteristics: a spoke pattern and a galaxy image.

Design, fabrication, and experimental demonstration of a diffractive optical element with long depth of field for nanoscale three-dimensional multi-molecule tracking

The development of real-time single-molecule detection and tracking technology in time and space for multiple bio-molecules in intact cells has important significance for the study on molecular behaviors in life processes. However, limited depth of field is the main drawback of conventional microscopy that prevents observation and tracking of multiple molecules in intact cells. Based on the principle of wavefront coding, the design and fabrication of a novel diffractive optical element (DOE) which combines a distorted diffraction grating with a double-helix point spread function (PSF) phase plate so that it can simultaneously perform multi-plane imaging with double-helix PSF and realize an extended depth of field is presented. Experiments have been carried out on a self-built microscopic system based on the novel DOE, showing that a depth of field can be up to 12 μm. Experimental results are in good agreement with the theoretical predictions, thus proving the feasibility of this method.

基于调制传递函数相似度的波前编码系统优化技术

基于调制传递函数相似度的波前编码系统优化技术