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Wavefront encoding (WFC) is a depth-of-field (DOF) extension technology that combines optical encoding and digital decoding. The system extends DOF at the expense of intermediate image quality and then decodes it through an image restoration algorithm to obtain a clear image. Affected by point spread differences, traditional decoding methods are often accompanied by artifacts and noise amplification problems. In this paper, based on lens-combined modulated wavefront coding (LM-WFC), we simulate the imaging process under different object distances, generate a simulation data set of WFC, and train a multi-scale convolutional neural network. The simulation experiment proves that this method can effectively reduce artifacts and improve image clarity. In addition, we used the LM-WFC camera to obtain real scene images with different target distances for experiments. The decoding results showed that the network model can enhance the quality of image restoration and generate clear images that are more in line with human vision, which is conducive to the improvement and practical application of wavefront coding systems. [ABSTRACT FROM AUTHOR]

Phase mask optimization is one of the critical steps in designing a wavefront coding system to extend the depth of field (DoF). As a classical phase mask, a cubic phase mask was taken as an example. An improved particle swarm optimization (PSO) algorithm was applied to calculate the parameters of the cubic phase mask by introducing the modulation transfer function as the optimization criterion and a threshold as a constraint. The quality of the subsequent image restoration is guaranteed on the premise of the extended DoF. Finally, the improved PSO was proved to be faster, more efficient, and more accurate compared to the simulated annealing algorithm and the traditional PSO. The experimental results verify that the cubic phase mask optimized by the improved PSO can achieve DoF extension in the wavefront coding system. The improved PSO can also be applied to other phase masks of wavefront coding systems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the novel method to improve the image quality for the optical imaging system with the radially symmetrical phase masks. By introducing 0-π phase mask into the radially symmetrical one, the new phase mask is generated, which produces the dark-shape point spread function. By rotating this phase mask with the amplitude mask for different angles, the point spread function is still rotated by the same angle. Moreover, the digital processing is used to restore the high-quality image. The simulation results demonstrated the effectiveness of the proposed method in comparison to the previously radially symmetrical phase mask. [ABSTRACT FROM AUTHOR]

The laser transport system of the high power laser facility is mainly composed of large-aperture laser transport mirrors (TMs). Obtaining the high-resolution online damage images during the operation, which is of great significance for operating safely of the mirrors and the facility. Based on wavefront coding, pan-tilt scanning and image stitching technologies, an online laser-damage images detection system is designed, and it can achieve high-precision detection of surface characteristics of large-aperture laser transport mirrors. The preliminary simulation proves that the system can solve the depth of field matching problem caused by pan-tilt tilt imaging and achieve higher resolution.

Phase mask optimization is one of the critical steps in designing a wavefront coding system to extend the depth of field (DoF). As a classical phase mask, a cubic phase mask was taken as an example. An improved particle swarm optimization (PSO) algorithm was applied to calculate the parameters of the cubic phase mask by introducing the modulation transfer function as the optimization criterion and a threshold as a constraint. The quality of the subsequent image restoration is guaranteed on the premise of the extended DoF. Finally, the improved PSO was proved to be faster, more efficient, and more accurate compared to the simulated annealing algorithm and the traditional PSO. The experimental results verify that the cubic phase mask optimized by the improved PSO can achieve DoF extension in the wavefront coding system. The improved PSO can also be applied to other phase masks of wavefront coding systems.

Wavefront coding is an effective way to extend the depth of field of optical imaging systems. The invariant defocusing imaging feature can be obtained by adding a phase mask with a suitable form to the aperture of a typical optical system. Traditional exponential phase mask defocusing optical characteristics exhibit strong invariance in the frequency domain, but the point spread function (PSF) variation is significant in the image plane To reduce PSF position deviation, we presented an improved exponential phase mask. The phase function of the improved mask is obtained by analyzing the relationship between Taylor expansion and wave aberration. Numerical analysis and imaging simulation are used to evaluate the performance of the proposed phase mask to that of other standard phase masks. The simulation results show that the improved exponential phase mask has a stronger defocus invariance of the modulation transfer function (MTF), and the position deviation of the PSF has been effectively controlled. [ABSTRACT FROM AUTHOR]

• A wavefront coding annular folded lens is presented in this paper which can achieve athermalization within the 100 °C range. • The relationship between obscuration radio and phase plate parameter is derived, which can be seen from the mathematical model that increased obscuration radio reduces PSF consistency. • A synthesized PSF is constructed using the genetic algorithm. High-quality image restoration over a wide temperature range with a single filter is enabled by the synthesized PSF. The annular folded lens (AFL) achieves miniaturization and integration of optical systems by single-element design. When over a wide temperature range, the AFL cannot be athermalized with one substrate material. In order to reduce the impact of temperature on imaging quality of the AFL, wavefront coding (WFC) technology is introduced. The WFC-AFL design principle is studied, the relationship between the obstruction ratio and the phase plate parameter is deduced, and the model of the obstruction ratio and the point spread function (PSF) consistency is established. In the digital decoding section, the image restoration effect of the PSF under different weights is studied, and the model of synthesized PSF is constructed using the genetic algorithm (GA). According to theory analysis, the infrared WFC-AFL with IRG26 is designed in the long-wave infrared 8 ∼ 12 μ m. The focal length is 50 mm, the total length is 18 mm, the F-number is 1 and the full field of view is 11° Image restoration with a single filter is achieved by using the synthetic PSF. For the restored images at -40 °C and 60 °C, the average SSIM values are improved by 0.0397 and 0.0141 respectively, the average PSNR values are improved by 1.9540db and 1.1077db respectively compared with common methods. The design provides a new idea for the athermalization of integrated and miniaturized optical systems. [ABSTRACT FROM AUTHOR]

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An incoherent optical system with wavefront coding extends the depth of field (DOF) by employing a cubic phase plate (CPP). We designed a digital microscope with a CPP in the aperture stop and on the surface of the lens, which extended the DOF. In addition, we proposed a method in which the CPP can be shifted and assigned to the surface of the lens by adjusting the third-order coefficient of the xy polynomial surface, so that the CPP on the surface of the lens can replace a single CPP in the aperture stop, which collided with the optical elements and mechanism in some cases, to reduce the difficulty in assembling. The microscope with flexibility and without loss of the illumination level can considerably improve the efficiency of microscopic applications.

Depth of field is an important factor of imaging systems that highly affects the quality of the acquired spatial information. Extended depth of field (EDoF) imaging is a challenging ill-posed problem and has been extensively addressed in the literature. We propose a computational imaging approach for EDoF, where we employ wavefront coding via a diffractive optical element (DOE) and we achieve deblurring through a convolutional neural network. Thanks to the end-to-end differentiable modeling of optical image formation and computational post-processing, we jointly optimize the optical design, i.e., DOE, and the deblurring through standard gradient descent methods. Based on the properties of the underlying refractive lens and the desired EDoF range, we provide an analytical expression for the search space of the DOE, which is instrumental in the convergence of the end-to-end network. We achieve superior EDoF imaging performance compared to the state of the art, where we demonstrate results with minimal artifacts in various scenarios, including deep 3D scenes and broadband imaging. [ABSTRACT FROM AUTHOR]

Wavefront coding is an effective way to extend the depth of field of optical imaging systems. The invariant defocusing imaging feature can be obtained by adding a phase mask with a suitable form to the aperture of a typical optical system. Traditional exponential phase mask defocusing optical characteristics exhibit strong invariance in the frequency domain, but the point spread function (PSF) variation is significant in the image plane To reduce PSF position deviation, we presented an improved exponential phase mask. The phase function of the improved mask is obtained by analyzing the relationship between Taylor expansion and wave aberration. Numerical analysis and imaging simulation are used to evaluate the performance of the proposed phase mask to that of other standard phase masks. The simulation results show that the improved exponential phase mask has a stronger defocus invariance of the modulation transfer function (MTF), and the position deviation of the PSF has been effectively controlled.

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. [ABSTRACT FROM AUTHOR]

The image deconvolution technique can recover potential sharp images from blurred images affected by aberrations. Obtaining the point spread function (PSF) of the imaging system accurately is a prerequisite for robust deconvolution. In this paper, a computational imaging method based on wavefront coding is proposed to reconstruct the wavefront aberration of a photographic system. Firstly, a group of images affected by local aberration is obtained by applying wavefront coding on the optical system’s spectral plane. Then, the PSF is recovered accurately by pupil function synthesis, and finally, the aberration-affected images are recovered by image deconvolution. After aberration correction, the image’s coefficient of variation and mean relative deviation are improved by 60% and 30%, respectively, and the image can reach the limit of resolution of the sensor, as proved by the resolution test board. Meanwhile, the method’s robust anti-noise capability is confirmed through simulation experiments. Through the conversion of the complexity of optical design to a post-processing algorithm, this method offers an economical and efficient strategy for obtaining high-resolution and high-quality images using a simple large-field lens.

We experimentally investigate the performance of co-optimized hybrid optical-digital imaging systems based on binary phase masks and digital deconvolution for extended depth-of-field (DoF) under narrowband illumination hypothesis. These systems are numerically optimized by assuming a simple generic imaging model. Using images of DoF targets and real scenes, we experimentally demonstrate that in practice, they actually reach the DoF range for which they have been optimized. Moreover, they are shown to be robust against small mask manufacturing errors and residual spherical aberration in the optical system. These results demonstrate that the optical/digital optimization protocol based on generic imaging model can be safely used to design DoF-enhanced imaging systems aimed at real-world applications. [ABSTRACT FROM AUTHOR]

• This paper analyzes the influence by defocus on the detection results of state-of-the-art object detection pipeline. • Simulation is conducted to demonstrate the superiority on accuracy rate using wavefront coding technique. • A novel wavefront coding method is proposed and a based imaging system is designed for extending the depth of field. • Comparison experiments are carried out to show the improvement on detection results by applying wavefront coding technique. 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. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract 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. 8 μ m 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. [ABSTRACT FROM AUTHOR]

Abstract Optical imaging systems with extended depth of field based on wavefront coding can be used in many fields, which require more object information along the optical axis in a snapshot. When using the non-rotational symmetric phase masks such as cubic phase mask, the final images are usually restored by classical wiener restoration method. However, the existence of image artifacts in final restored images is a problem to be solved. We proposed a method to alleviate the image artifacts by processing two conjugate images, which are captured by image sensor before and after rotating the phase mask 180 degrees along the optical axis. Unlike the previous methods usually need to measure the point spread function or optical transfer function of the imaging system, we do not need to measure them anymore. Both the ZEMAX simulation and experiment verified our method. [ABSTRACT FROM AUTHOR]

This paper introduces a novel lensless full colour diffractive computational imaging system with a planar Multilevel Phase Mask (MPM) as a diffractive optical element (DOE). The novelty concerns: a methodology of MPM design for improved depth of focus (DoF); design of PSFs for RGB imaging and an inverse imaging algorithm with sparse colour image modelling simultaneous for all RGB channels. MPMs are step-wise invariant. The cubic wavefront coding (WFC) is incorporated in MPMs with optimization of number of levels and width of invariant steps. This design of MPM makes the system robust with respect to defocus (improves DoF) and diminish chromatic aberrations typical for DOEs. Broadband multichannel test-images are exploited for design and testing of the lensless system. We consider two alternative optical setups: Wavelength Multiplexing (WM) and Wavelength Division (WD). In WM, the light beam is broadband multichannel with light sources radiating all wavelengths simultaneously and a CMOS sensor is equipped with a Bayer colour filter array (CFA) for registration of spectral measurements. In this setup, a single MPM is designed for the broadband multichannel light beams. In WD, separate exposures of RGB channels are registered by a broadband grey-scale CCD sensor. Different MPMs are designed for each of the RGB channels. Simulation experiments demonstrate the essentially extended DoF of the designed lensless systems and the advanced accuracy and quality of imaging with respect to the corresponding WM and WD systems with refractive lenses. Due to robustness of the designed lensless system to chromatic aberrations, this advantage has a place even with respect to the lens-system. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

Optimization of the phase mask is one of the key tasks in the design of wavefront coding systems for depth of field extension. Instead of optimization of the phase mask for ideal optical systems, which was the focus of the previous research, this paper proposes an integrative optimization method for practical optical systems considering the various optical aberrations. A practical wavefront coding system based on a doublet is designed using the integrative optimization method, while an ideal system with an optimized phase mask is also used for comparison. The simulation results show that the practical wavefront coding system designed by the integrative optimization method works well on both the on-axis and off-axis fields, while the ideal system with the optimized phase mask had a poor performance on the off-axis fields. Off-axis fields should also be considered as well as on-axis field in the design of practical optical systems, therefore the integrative optimization method will be significant for the design of practical wavefront coding systems. [ABSTRACT FROM AUTHOR]

110 °C range athermalization is significant but difficult for designing infrared imaging systems. Our wavefront coding athermalized infrared imaging system adopts an optical phase mask with less manufacturing errors and a decoding method based on shrinkage function. The qualitative experiments prove that our wavefront coding athermalized infrared imaging system has three prominent merits: (1) working well over a temperature range of 110 °C; (2) extending the focal depth up to 15.2 times; (3) achieving a decoded image being approximate to its corresponding in-focus infrared image, with a mean structural similarity index (MSSIM) value greater than 0.85. [ABSTRACT FROM AUTHOR]

Color coding has been experimentally demonstrated to be able to extend the depth of field (DoF) of an imaging system in single snapshot. A numerical model is adopted in this paper to quantitatively characterize its imaging properties (strehl ratio, point spread function and modulation transfer function). To improve the system’s performance under nonuniform spectrum, we proposed to introduce wavefront coding into the system. Numerical results show that wavefront coding acts as an average filter of the spectrum, so that it is able to get an almost invariant MTF across the focal line even under nonuniform spectrum, which is desirable in many applications. [ABSTRACT FROM AUTHOR]

Imaging characteristics of wavefront coding systems in the presence of spherical aberration are analyzed by using ray aberration approach. The analytical expressions for ray aberration, the boundary of ray map and the size of spot diagram of a wavefront coding system in the presence of defocus and spherical aberration are obtained by wave aberration theory. The effect of spherical aberration on imaging performance of wavefront coding systems with a cubic phase mask is presented by ray aberration and spot diagram. The results show that the wavefront coding systems have a high tolerance to spherical aberration through a given defocus range. [ABSTRACT FROM AUTHOR]

For many practical applications of image sensors, how to extend the depth-of-field (DoF) is an important research topic; if successfully implemented, it could be beneficial in various applications, from photography to biometrics. In this work, we want to examine the feasibility and practicability of a well-known "extended DoF" (EDoF) technique, or "wavefront coding," by building real-time long-range iris recognition and performing large-scale iris recognition. The key to the success of long-range iris recognition includes long DoF and image quality invariance toward various object distance, which is strict and harsh enough to test the practicality and feasibility of EDoF-empowered image sensors. Besides image sensor modification, we also explored the possibility of varying enrollment/testing pairs. With 512 iris images from 32 Asian people as the database, 400-mm focal length and F/6.3 optics over 3 m working distance, our results prove that a sophisticated coding design scheme plus homogeneous enrollment/testing setups can effectively overcome the blurring caused by phase modulation and omitWiener-based restoration. In our experiments, which are based on 3328 iris images in total, the EDoF factor can achieve a result 3.71 times better than the original system without a loss of recognition accuracy. [ABSTRACT FROM AUTHOR]

Freeform surfaces are being developed for number of applications like illumination systems, compact projection systems, head up display, ophthalmic and automotive industries. One of the important use of such surfaces in optical imaging application is wavefront coding for large depth of focus camera. The thermal induced defocus is the well-known problem in infrared (IR) imaging systems. The efficient technique to mitigate the effect of defocus is wavefront coding, The phase profile for wavefront coding application with IR camera is a cubic freeform profile, that enables the focus invariant across the region near the focal plane. This work presents the development of a high precision cubic freeform profile on Germanium (Ge) substrate and its application for extended depth of focus for IR imaging camera. The cubic freeform profile on the surface is generated using single point diamond turning (SPDT) in slow tool servo (STS) configuration. It is further polished by using bonnet polisher with polyurethane and uninap-13 pads in seven axis polishing machine. The precise work piece alignment during the generation and characterization of the surface is very important aspect which is taken care by introducing fiducials from the beginning of the process of realization of the component. Full field measurement of grinded surface is carried out by using long wavelength interferometer. Computer generated hologram (CGH) in Fizeau interferometer is used for corrective polishing metrology and final testing of the surface profile. Precise work piece alignment and full field measurement starting from the grinding stage helped to achieve surface with residual error of 0.2 µm PV and 1.4 nm RMS roughness (Rq). The developed cubic profile is used in infrared camera for wavefront coding in an experimental setup for the verification of the intended results. [ABSTRACT FROM AUTHOR]

Wavefront coding is an effective way to extend the depth of field of an incoherent imaging system. With a suitable phase mask, the defocus invariant imaging characteristic of an incoherent imaging system can be achieved. In this paper, an effective way to generate new type of phase mask is proposed. On the basis of the new method, the inverse sinusoidal phase mask is proposed to enrich the family of anti-symmetric phase masks. The performances of inverse sinusoidal phase mask are evaluated by comparisons with cubic, sinusoidal and tangent phase masks. Numerical evaluations demonstrate that the proposed phase mask has superior performance in extending the depth of field and small artifacts in restored images, particularly at large defocus. [ABSTRACT FROM AUTHOR]

Wavefront coding is an effective optical technique used to extend the depth of field for an incoherent imaging system. Through introducing an optimized phase mask to the pupil plane, the modulated optical transfer function is defocus-invariant. In this paper, we proposed a new form phase mask using non-integer order and signum function to extend the depth of field. The performance of the phase mask is evaluated by comparing defocused modulation transfer function invariant and Fisher information with other phase masks. Defocused imaging simulation is also carried out. The results demonstrate the advantages of non-integer order phase mask and its effectiveness on the depth of field extension. [ABSTRACT FROM AUTHOR]

The point spread function (PSF) inconsistency caused by temperature variation leads to artifacts in decoded images of a wavefront coding infrared imaging system. Therefore, this paper proposes an analytical model for the effect of temperature variation on the PSF consistency. In the proposed model, a formula for the thermal deformation of an optical phase mask is derived. This formula indicates that a cubic optical phase mask (CPM) is still cubic after thermal deformation. A proposed equivalent cubic phase mask (E-CPM) is a virtual and room-temperature lens which characterizes the optical effect of temperature variation on the CPM. Additionally, a calculating method for PSF consistency after temperature variation is presented. Numerical simulation illustrates the validity of the proposed model and some significant conclusions are drawn. Given the form parameter, the PSF consistency achieved by a Ge-material CPM is better than the PSF consistency by a ZnSe-material CPM. The effect of the optical phase mask on PSF inconsistency is much slighter than that of the auxiliary lens group. A large form parameter of the CPM will introduce large defocus-insensitive aberrations, which improves the PSF consistency but degrades the room-temperature MTF. [ABSTRACT FROM AUTHOR]

We introduce a scanless optical method to image neuronal activity in three dimensions simultaneously. Using a spatial light modulator and a custom-designed phase mask, we illuminate and collect light simultaneously from different focal planes and perform calcium imaging of neuronal activity in vitro and in vivo. This method, combining structured illumination with volume projection imaging, could be used as a technological platform for brain activity mapping.

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. [ABSTRACT FROM AUTHOR]

Wavefront coding involves the use of an asymmetrical phase mask to extend the depth of field of incoherent imaging systems. The performance of wavefront coding systems depends on designing a suitable phase profile to generate the defocus-invariant imaging characteristic. We proposed a square-root phase mask with two profile factors for achieving a steadier defocused modulation transfer function (MTF). Several evaluation methods are employed for the purpose of performance comparison between the proposed phase mask and the previously suggested phase masks under the constraint condition that the phase parameters are optimized at the same level of noise gain. Numerical results show that the square-root phase mask yields better properties in extended depth of field imaging, especially in acquiring defocus-invariant MTFs and eliminating image artifacts associated with the decoded images. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]