Wavefront Coding Technique Research Articles

Chromatic Aberration in Wavefront Coding Imaging with Trefoil Phase Mask

The refractive index of the lenses used in optical designs varies with wavelength, causing light rays to fail when focusing on a single plane. This phenomenon is known as chromatic aberration (CA), chromatic distortion, or color fringing, among other terms. Images affected by CA display colored halos and experience a loss of resolution. Fully achromatic systems can be achieved through complex and costly lens designs and/or computationally when digital sensors capture the image. In this work, we propose using the wavefront coding (WFC) technique with a trefoil-shaped phase modulation plate in the optical system to effectively increase the resolution of images affected by longitudinal chromatic aberration (LCA), significantly simplifying the optical design and reducing costs. Experimental results with three LEDs simulating RGB images verify that WFC with trefoil phase plates effectively corrects longitudinal chromatic aberration. Transverse chromatic aberration (TCA) is corrected computationally. Furthermore, we demonstrate that the optical system maintains depth of focus (DoF) for color images.

Decoupled illumination detection in light sheet microscopy for 4D observation of spermatozoa at high-resolutions

We present the use of wavefront coding (WFC) combined with machine learning in a light sheet fluorescence microscopy (LSFM) system. We visualize the 3D dynamics of sperm flagellar motion at an imaging speed up to 80 volumes per second, which is faster than twice volumetric video rate. By using the WFC technique we achieve to extend the depth of field of the collection objective with high numerical aperture (NA=1) from 2.6 μm to 50 μm, i. e., more than one order of magnitude. To improve the quality of the final images, we applied a machine learning-based algorithm to the acquired sperm raw images and to the point spread function (PSF) of the generated cubic phase masks previous to the deconvolution process.

Correcting the effect of temperature on image quality of thermal imaging objectives by wavefront coding technique

The paper has proposed a method for correcting the effect of temperature on the imaging quality of thermal imaging systems by wavefront coding technology. A cubic phase mask was added to the aperture diaphragm of the thermal imaging objective to obtain a temperature-invariant point spread function (PSF). The received images will be of low quality but almost invariant with the change in temperature. An inverse filter was used to recover high-quality images over a variable temperature range. To demonstrate the effectiveness of the proposed method, a thermal imaging objective was used to experiment. The simulation results demonstrate that the proposed method can effectively eliminate the temperature influence on the image quality of the thermal imaging objective.

Wavefront Coding See-Through Display with Extension of Depth of Field

We propose a see-through display with a wavefront coding (WFC) technique using a cubic phase plate to extend the depth of field (DOF) of the projected virtual image. The image projected by the WFC see-through display allows the eyes to see an object in the range of accommodation and a clear projected image simultaneously without re-focusing. The DOF of the clear projected image by the system can be extended from 250 mm to an optical infinity of 10 m.

PARAMETRIC BLIND-DECONVOLUTION METHOD TO REMOVE IMAGE ARTIFACTS IN WAVEFRONT CODING IMAGING SYSTEMS

Wavefront coding technique includes a phase mask of asymmetric phase mask kind in the pupil plane to extend the depth of field of an imaging system and the digital processing step to obtain the restored final high-quality image. However, the main drawback of wavefront coding technique is image artifacts on the restored final images. In this paper, we proposed a parameter blind-deconvolution method based on maximizing of the variance of the histogram of restored final images that enables to obtain the restored final image with artifact-free over a large range of defocus.

Extended Depth-of-Field of a Miniature Optical Endoscope Using Wavefront Coding

Endoscopic imaging is an indispensable tool for visual inspection of surfaces in hard-to-access places. The conventional optical endoscope only enables imaging the regions that lie close to the focal plane, and therefore improving the depth of field (DOF) of an endoscopic system has recently attracted much attention. Here, we propose and demonstrate a simple, cost-effective, and easily available industrial endoscopic system, which is composed of a rigid tube and group of optical lenses. The outer diameter of the designed endoscopic modality presented in this article is 3 mm. By employing the wavefront coding technique, the DOF of newly-designed endoscope was extended to 2.7 mm in the proof-of-concept experiment, which is an increase of almost 10 times compared to the initial counterpart.

Investigation of extended depth-of-field f/8 camera with optimized cubic phase mask and digital restoration

An investigation of extended depth-of-field camera with optimized phase mask and digital restoration is presented. The goal of this paper is to implement the wavefront coding technique without affecting much of the original design, and the design has taken the complexity of imaging system into consideration. The optimized strength of cubic phase mask (CPM) is based on the analytical optimal solution for the task-based imaging system [J. Opt. Soc. Am. A 25, 1064 (2008)]. The noisy intermediate images of CPM system with highest spatial frequency of interest can be effectively restored by vector-based Richardson-Lucy algorithm. Restoration from the system with generalized CPM produces precise image position than the system with CPM does. In general, the CPM system procures modulation transfer function higher than 0.195 in the whole depth-of-field, and the mean squared error of the restored images are less than 5 %.

Extended-depth-of-field object detection with wavefront coding imaging system

As an important issue in the field of computer vision, object detection has broad application prospects. Recent researches using convolutional neural networks (CNN) have shown the state-of-the-art results in the challenge competition. Most of them focused on improving the precision under ideal imaging conditions. However, it is hard to ensure that the optical imaging system works in the focused state in practice. In this study, we examine the impact of defocus on detection accuracy. The results show that even the state-of-the-art network is sensitive to a different defocus situation. Thus we put forward wavefront coding (WFC) technique for improving the performance over a large range of depth of field (DOF). Simulation results indicate the improvement on average precision of detection results by applying WFC. In addition, we propose a novel WFC method for overcoming the defects of the traditional one. Then the optical imaging system is designed under the guidance of the proposed theory. Experiments are conducted to suggest that the detection accuracy rate can be enhanced considerably with WFC.

Athermalization of infrared optical system through wavefront coding

Owing to the thermal effect of optical components, it has been challenging for conventional infrared optical imaging system to work in a large temperature range. Wavefront coding technique has been shown to greatly increase tolerance to manufacturing inaccuracies and various defocus, particularly thermal defocus. In this paper, we develop an entirely new infrared imaging modality in 3.7 ∼4.8μm waveband, realized with a secondary imaging structure, a non-rotationally symmetric phase mask and a cooled infrared focal plane arrays. The proposed system offers the ability to overcome the temperature limitations of conventional infrared system as well as effectively eliminate the thermal aberration. Proof-of-concept results demonstrate significantly our athermalized optical system perform high-quality images in the operation temperature range of −40 °C to 70 °C.

Optimized Asymmetrical Arcsine Phase Mask for Extending the Depth of Field

With the development of wavefront coding technique, various x-y separable phase masks have been proposed for the purpose of extending the depth of field. In this letter, a new asymmetrical arcsine phase mask combing the power and arcsine function was proposed to enrich the separable odd symmetrical family of wavefront coding phase masks. Using the simulated annealing algorithm based on Fisher information for optimization, we evaluated the performance of arcsine phase mask with four typical phase masks: the tangent, sinusoidal, improved-2 logarithmic, and cubic phase masks. The comparison results of Fisher information, defocused modulation transfer function, Hilbert space angle, and digital restoration demonstrated that the arcsine phase mask could restore clear and homogeneous images with both high fidelity and high signal to noise ratio along with a wide range of defocus, proving its superiority in extending the depth of field.

Design and numerical simulation demonstration of multi-functional holographic phase plate for large depth of field single molecular localization microscopy

The development of nanoscale single-molecule localization and tracking technology for multiple bio-molecules in intact cells has important significance for studying the dynamic process in life process. Since most of cells are several microns in depth, but the focal depth of traditional optical microscopes are less than one micron, the limited depth of field is the main drawback of conventional single molecular localization microscopy that prevents observation and tracking of multiple molecules in intact cells. In this paper, based on the wavefront coding technique, a new type of holographic phase plate with high efficiency is proposed and designed to extend the depth of field of single molecular localization microscopy, which combines the distorted multi-value pure-phase grating (DMVPPG) with the double-helix point spread function (DH-PSF). The DMVPPG can be used to realize multiplane imaging of several tens of layers of a sample in a single detection plane. And the DH-PSF is an engineered point spread function which encodes the lateral and axial position with high precision of a molecule in the center of its two lobes and the angle between them respectively. Using the combined holographic phase plate, the molecules in dozens layers of a whole cell can be simultaneously imaged on the same detection plane with DH-PSF. Not only can the axial resolving power be improved, but the imaging depth can also be extended without scanning. Adding such a holographic phase plate to the imaging path, the limited imaging depth problem in single-molecule-localization microscopy can be solved without sacrificing the localization accuracy. The proposed new type of holographic phase plate can also be implemented with a spatial light modulator. In the following numerical simulation experiments, the designed holographic phase plate is composed of 600×600 pixels with a pixel size of 10 μm. The distance between two adjacent focal planes is designed to be 0.5 μm. Such a holographic phase plate is placed on the Fourier transform plane of the detection light path. When an emitter is located on the focal plane, it can be imaged as two lobes without rotation in a center area of the field of view. If an emitter is -6 μm away from the focal plane, the DH-PSF appears in the upper-left area of the field of view. Simulation results demonstrate that a total of 25 sample layers can be simultaneously imaged on the single detection plane and the 12 μm detection range can be achieved, thus proving the feasibility of this method.

Reduction of artefacts and noise for a wavefront coding athermalized infrared imaging system

Because of obvious drawbacks including serious artefacts and noise in a decoded image, the existing wavefront coding infrared imaging systems are seriously restricted in application. The proposed ultra-precision diamond machining technique manufactures an optical phase mask with a form manufacturing errors of approximately 770 nm and a surface roughness value Ra of 5.44 nm. The proposed decoding method outperforms the classical Wiener filtering method in three indices of mean square errors, mean structural similarity index and noise equivalent temperature difference. Based on the results mentioned above and a basic principle of wavefront coding technique, this paper further develops a wavefront coding infrared imaging system. Experimental results prove that our wavefront coding infrared imaging system yields a decoded image with good quality over a temperature range from −40 °C to +70 °C.

Optimization of Wavefront Coding Phase Mask Applied to 5X-40X Micro-Objectives Simultaneously

A wavefront coding (WFC) technique provides an extension of the depth of field for a microscopy imaging system with slight loss of image spatial resolution. Through the analysis of the relationship between the incidence angle of light at the phase mask and the system pupil function, a mixing symmetrical cubic phase mask (CPM) applied to 5X-40X micro-objectives is optimized simultaneously based on point-spread function (PSF) invariance and nonzero mean values of the modulation transfer function (MTF) near the spatial cut-off frequency. Optimization results of the CPM show that the depth of field of these micro-objectives is extended 3-10 times respectively while keeping their resolution. Further imaging simulations also prove its ability in enhancing the defocus imaging.

Odd symmetrical square-root phase mask to extend the depth of field in wavefront-coded imaging systems

Extend-the-depth-of-field imaging can be achieved by wavefront coding technique, which inserts an odd symmetrical phase mask into the pupil plane to generate the invariant imaging property over a wide range of defocus. Obtaining the low sensibility to defocus for wavefront coding systems depends on designing a proper phase profile. Here we proposed a phase mask combining the power function with the square-root function to maximize the invariant imaging property to defocus. Judging by defocused modulation transfer function (MTF) and Hilbert space angle, numerical comparisons with the cubic mask, exponential mask and improved logarithmic mask prove the superiority of proposed square-root phase mask in extending the depth of field.

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.

A three‐dimensional multifunctional compound‐eye endoscopic system with extended depth of field

AbstractA focusing‐free and multispectral three‐dimensional endoscope based on a compact compound‐eye camera is proposed. A prototype TOMBO endoscope with 3 ×2 aspherical lenses using a wavefront coding technique and a 640 ×480‐pixel color imager demonstrates extended depth of field and registration of multispectral images based on an estimated depth map. © 2012 Wiley Periodicals, Inc. Electron Comm Jpn, 95(11): 14–27, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/ecj.11431

Analytical and experimental demonstration of depth of field extension for incoherent imaging system with a standard sinusoidal phase mask

The wavefront coding technique is used to enlarge the depth of field (DOF) of incoherent imaging systems.The key to wavefront coding lies in the design of suitable phase masks. To date, numerous kinds of phase masks are proposed. However, further understanding is needed regarding phase mask with its phase function being in a standard sinusoidal form. Therefore, the characteristics of such a phase mask are studied in this letter. Deriving the defocused optical transfer function (OTF) analytically proves that the standard sinusoidal phase mask is effective in extending the DOF, and actual experiments confirm the numerical results. At the same time, with the Fisher information as a criterion, the standard sinusoidal phase mask shows a higher tolerance to focus errors (especially severe focus errors) than the classical cubic phase mask.

Wavefront coding technique for controlling thermal defocus aberration in an infrared imaging system

We use a wavefront coding approach to control thermal defocus aberration in an IR imaging system. The design method of athermalized system using a wavefront coding technique is discussed. An athermalized long wave IR optical system, which works at temperatures ranging from -40 °C to 60 °C, is designed by employing a cubic phase mask. Computer simulations and the first experimental demonstration are executed to verify the performance of this wavefront coded athermalized system and to clarify the issues related to its implementation.

Simple PSF based method for pupil phase mask’s optimization in wavefront coding system

By applying the wavefront coding technique to an optical system, the depth of focus can be greatly increased. Several complicated methods, such as Fisher Information on based method, have already been taken to optimize for the best pupil phase mask in ideal condition. Here one simple point spread function (PSF) based method with only the standard deviation method used to evaluate the PSF stability over the depth of focus is taken to optimize for the best coefficients of pupil phase mask in practical optical systems. Results of imaging simulations for optical systems with and without pupil phase mask are presented, and the sharpness of image is calculated for comparison. The optimized results showed better and much more stable imaging quality over the original system without changing the position of the image plane.