Experimental study of an off-axis three mirror anastigmatic system with wavefront coding technology

Wavefront coding (WFC) is a kind of computational imaging technique that controls defocus and defocus related aberrations of optical systems by introducing a specially designed phase distribution to the pupil function. This technology has been applied in many imaging systems to improve performance and/or reduce cost. The application of WFC technology in an off-axis three mirror anastigmatic (TMA) system has been proposed, and the design and optimization of optics, the restoration of degraded images, and the manufacturing of wavefront coded elements have been researched in our previous work. In this paper, we describe the alignment, the imaging experiment, and the image restoration of the off-axis TMA system with WFC technology. The ideal wavefront map is set to be the system error of the interferometer to simplify the assembly, and the coefficients of certain Zernike polynomials are monitored to verify the result in the alignment process. A pinhole of 20 μm diameter and the third plate of WT1005-62 resolution patterns are selected as the targets in the imaging experiment. The comparison of the tail lengths of point spread functions is represented to show the invariance of the image quality in the extended depth of focus. The structure similarity is applied to estimate the relationship among the captured images with varying defocus. We conclude that the experiment results agree with the earlier theoretical analysis.     

Lensless broadband diffractive imaging with improved depth of focus: wavefront modulation by multilevel phase masks

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.     

Effect of illumination in an integral imaging system with large depth of focus

We present the characteristics of integral imaging systems with large depth of focus (DOF) by use of two kinds of illumination: plane illumination and diffusing illumination. For each system, we perform ray analysis based on ray optics. To check the visual quality through optical experiments, we use an average image of observed images picked up at various positions within a large DOF. The synthesized elemental images for a three-dimensional (3-D) object with two character patterns were displayed in an optical system and its reconstruction experiments are performed. Experimental results show that use of diffusing illumination can improve visual quality of reconstruction 3-D images in depth-priority integral imaging.     

Task-based lens design with application to digital mammography

Recent advances in model observers that predict human perceptual performance now make it possible to optimize medical imaging systems for human task performance. We illustrate the procedure by considering the design of a lens for use in an optically coupled digital mammography system. The channelized Hotelling observer is used to model human performance, and the channels chosen are differences of Gaussians. The task performed by the model observer is detection of a lesion at a random but known location in a clustered lumpy background mimicking breast tissue. The entire system is simulated with a Monte Carlo application according to physics principles, and the main system component under study is the imaging lens that couples a fluorescent screen to a CCD detector. The signal-to-noise ratio (SNR) of the channelized Hotelling observer is used to quantify this detectability of the simulated lesion (signal) on the simulated mammographic background. Plots of channelized Hotelling SNR versus signal location for various lens apertures, various working distances, and various focusing places are presented. These plots thus illustrate the trade-off between coupling efficiency and blur in a task-based manner. In this way, the channelized Hotelling SNR is used as a merit function for lens design.     

Improving photon count and flat profiles of multiplex imaging systems with the odd-symmetric quadratic phase modulation mask

The odd-symmetric quadratic (OSQ) phase mask is examined as a candidate for reduction of working distance and enhancement of light collection in multiplex imaging systems. The knowledge gained from the exact mathematical representation of the optical transfer function of the OSQ phase mask imager is exploited to explain the limits of system performance and quantify the upper bound on the magnitude of defocus within which this wavefront coding imager can successfully operate. The sensitivity of this imaging system to defocus about the special imaging condition that yields an enhanced dynamic range is examined, and it is shown that the modulation transfer function (MTF) degradation when the magnitude of misfocus is increased past this condition is much more gradual than the degradation of a conventional imager past a zero-misfocus state. The condition required for the spatial frequency and angular resolution of this OSQ phase mask imager to exceed that of its counterpart scaled imager is established, and results of simulated imaging under a reduced working distance configuration are presented.     

Aberration-free superresolution imaging via binary speckle pattern encoding and processing

We present an approach that provides superresolution beyond the classical limit as well as image restoration in the presence of aberrations; in particular, the ability to obtain superresolution while extending the depth of field (DOF) simultaneously is tested experimentally. It is based on an approach, recently proposed, shown to increase the resolution significantly for in-focus images by speckle encoding and decoding. In our approach, an object multiplied by a fine binary speckle pattern may be located anywhere along an extended DOF region. Since the exact magnification is not known in the presence of defocus aberration, the acquired low-resolution image is electronically processed via a parallel-branch decoding scheme, where in each branch the image is multiplied by the same high-resolution synchronized time-varying binary speckle but with different magnification. Finally, a hard-decision algorithm chooses the branch that provides the highest-resolution output image, thus achieving insensitivity to aberrations as well as DOF variations. Simulation as well as experimental results are presented, exhibiting significant resolution improvement factors.     

Chirp-coded excitation imaging with a high-frequency ultrasound annular array

High-frequency ultrasound (HFU, > 15 MHz) is an effective means of obtaining fine-resolution images of biological tissues for applications such as opthalmologic, dermatologic, and small animal imaging. HFU has two inherent drawbacks. First, HFU images have a limited depth of field (DOF) because of the short wavelength and the low fixed F-number of conventional HFU transducers. Second, HFU can be used to image only a few millimeters deep into a tissue because attenuation increases with frequency. In this study, a five-element annular array was used in conjunction with a synthetic-focusing algorithm to extend the DOF. The annular array had an aperture of 10 mm, a focal length of 31 mm, and a center frequency of 17 MHz. To increase penetration depth, 8-micros, chirp-coded signals were designed, input into an arbitrary waveform generator, and used to excite each array element. After data acquisition, the received signals were linearly filtered to restore axial resolution and increase the SNR. To compare the chirpcoded imaging method with conventional impulse imaging in terms of resolution, a 25-microm diameter wire was scanned and the -6-dB axial and lateral resolutions were computed at depths ranging from 20.5 to 40.5 mm. The results demonstrated that chirp-coded excitation did not degrade axial or lateral resolution. A tissue-mimicking phantom containing 10-microm glass beads was scanned, and backscattered signals were analyzed to evaluate SNR and penetration depth. Finally, ex vivo ophthalmic images were formed and chirpcoded images showed features that were not visible in conventional impulse images.     

Generalized signal-to-noise ratio for spectral sensors with correlated bands

Traditional spectral sensors are intentionally designed to minimize overlap among spectral response functions of different bands. In contrast, some emerging classes of spectral sensors exhibit significant band overlap. An effect introduced by such band overlap is that the photodetector noise of one band is coupled into the others in subsequent data processing steps. Because of this, the traditional band-by-band definition of signal-to-noise ratio (SNR) cannot fully describe the detector's noise level. We devise a general definition of SNR in spectral space based on a recently developed geometrical spectral imaging model [J. Opt. Soc. Am. A24, 2864 (2007)]. With this model, we can find an orthogonal basis of the spectral response functions for the spectral sensor with decreasing instrument SNRs. We can also define the average instrument SNR for the whole sensor, which makes it possible to characterize quantitatively the photodetector noise of a spectral sensor with correlated bands.     

Flexible depth-of-field imaging system using a spatial light modulator

A major problem of optical microscopes is their small depth-of-field (DOF), which hinders automation of micro object manipulation using visual feedback. Wavefront coding, a well-known method for extending DOF, is not suitable for direct application to micro object manipulation systems based on visual feedback owing to its expensive computational cost and due to a trade-off between the DOF and the image resolution properties. To solve such inherent problems, a flexible DOF imaging system using a spatial light modulator in the pupil plane is proposed. Especially, the trade-off relationship is quantitatively analyzed by experiments. Experimental results show that, for low criterion resolution, the DOF increases as the strength of the mask increases, while such a trend was not found for high criterion resolution. With high criterion resolution, the DOF decreases as the mask strength increases when high-resolution images are required. The results obtained can be used effectively to find the optimum mask strength given the desired image resolution.     

Experimental realization of an imaging system with an extended depth of field

We describe the experimental realization of an all-optical imaging system with an extended depth of field (DOF). The core of the system is a phase mask consisting of 16 Fresnel lenses (FLs) that are spatially multiplexed and mutually exclusive. Because each FL, in tandem with the primary lens, is designed to produce a sharp image for a specific object plane location, jointly the FLs achieve a wide DOF. However, the resultant image exhibits reduced resolution. The acquired image, onto which we did not apply any postprocessing, clearly is sharper than that acquired with a clear-aperture imaging system with the same pupil size.     

Wide-angle narrow-bandpass optical detection system optimally designed to have a large signal-to-noise ratio

A method for achieving optimal design of a wide-angle narrow-bandpass optical detection system composed of a spherical interference filter and a circular photodetector is introduced. It was found that there is an optimal photodetector diameter that maximizes the signal-to-noise ratio (SNR) for a given filter configuration. We show how to optimize optical detection systems based on spherical interference filters for all the important parameters simultaneously. The SNR values of these systems are compared with the SNR values of spherical-step-filter-based detection systems. When large silicon photodetectors are used, the two systems have equal SNR values so that the more economical step-filter systems are preferable. The results given here in the near-infrared region can be used for the optimization of any configuration of a detection system based on a spherical interference filter and a silicon photodetector working at the same wavelength range, without further calculations.     

Defocus from depth for defocus measurement

A novel method is proposed for defocus map estimation. It is based on the defocus origin that is essentially the reverse of depth from defocus (DFD). The main relations among image defocus, sensor defocus, and scene defocus for an imaging system are introduced. A defocus map is deduced from the depth map and the depth map is derived from the disparity map. The full disparity map can be reconstructed using an image-matching method and our clustering segmentation algorithm. Experimental results for an interior scene and an outdoor scene demonstrate that our method is effective in defocus measurement.     

Partially coherent light-emitting diode illumination for video-rate in-line holographic microscopy

The light of a light-emitting diode or a common thermal source, such as a tungsten filament lamp, is known to be quasi-incoherent. We generated partially coherent light of these sources with a volume of coherence in the micrometer range of 5-100 μm3 by spatial and spectral filtering. The corresponding degree of partial coherence was adapted for microscopic interference setups, such as a digital in-line holographic microscope. The practicability of the sources was determined by the spectral emittance and the resulting signal-to-noise ratio (SNR) of the detector. The microscale coherence in correlation with the SNR and its resolution for microscopy were analyzed. We demonstrate how low-light-level, non-laser sources enable holographic imaging with a video frame rate (25 frames/s), an intermediate SNR of 8 dB, and a volume of coherence of 3.4×10(4) μm3. Holograms of objects with a lateral resolution of 1 μm were achieved using a microscope lens (50×/NA=0.7) and a CCD camera featuring a 4-12 bit dynamic range.     

Simultaneous multiplane imaging with a distorted diffraction grating

We describe a simple technique for simultaneously imaging multiple layers within an object field onto a single camera. The approach uses a binary diffraction grating in which the lines are distorted such that a different level of defocus is associated with each diffraction order. The design of the gratings is discussed, and their ability to image multiple object planes is validated experimentally. Extension of the technique for spherical-aberration correction is described, and it is shown how the gratings can be used as part of a wave-front-sensing system.     

Defocus transfer function for circularly symmetric pupils

We present a two-dimensional function that graphically illustrates the effects of defocus on the optical transfer function (OTF) associated with a circularly symmetric pupil function. We call it the defocus transfer function (DTF). The function is similar in application to the ambiguity function, which can be used to display the OTF associated with a defocused rectangularly separable pupil function. The properties of the DTF make it useful for analyzing optical systems with circularly symmetric pupils when one is interested in the OTF as a function of defocus. In addition to presenting these properties, we give examples of the DTF for systems with clear, bifocal, and annular pupil functions.     

Effects of axial, transverse, and oblique sample motion in FD OCT in systems with global or rolling shutter line detector

This study deals with effects on the interference signal caused by axial, transverse, and oblique motion in spectrometer-based Fourier-domain optical coherence tomography (FD OCT). Two different systems are compared-one with a global shutter line detector and the other with a rolling shutter. We present theoretical and experimental investigations of motion artifacts. Regarding axial motion, fringe washout is observed in both systems, and an additional Doppler frequency shift is seen in the system using a rolling shutter. In addition, both systems show the same SNR decrease as a result of a transversely and obliquely moving sample. The possibility of flow measurement by using the decrease in signal power was demonstrated by imaging 1% Intralipid emulsion flowing through a glass capillary. This research provides an understanding of the SNR degradation caused by sample motion and demonstrates the importance of fast data acquisition in medical imaging.     

Liquid tunable lens integrated with a rotational symmetric surface for long depth of focus

A liquid tunable lens with an extended depth of focus (DOF) is proposed. By integrating a phase plate with rotational symmetric quartic function (QF) contour into the liquid lens cavity, the lens can achieve higher tolerance to the defocus aberration. The liquid lens was fabricated with a convenient and low-cost process that combined single-point diamond turning (SPDT) with soft lithography using polydimethylsiloxane (PDMS). Experimental results demonstrate that both focal length tunability and extended DOF can be achieved with the proposed liquid lens.     

Signal-to-noise ratio for astronomical imaging by deconvolution from wave-front sensing

One method for improving the quality of astronomical images measured through a atmospheric turbulence uses simultaneous short-exposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function, which is then used in a deconvolution procedure. This imaging method has been called both deconvolution from wave-front sensor (DWFS) measurements and self-referenced speckle holography. We analyze the signal-to-noise ratio (SNR) behavior of this imaging method in the spatial frequency domain. The analysis includes effects arising from differences in the correlation properties of the incident and the estimated pupil phases and the fact that the object-spectrum estimator is a randomly filtered doubly stochastic Poisson random process. SNR resultsobtained for the DWFS method are compared with the speckle-imaging powerspectrum SNR for equivalent seeing conditions and light levels. It is shown that for unresolved stars the power-spectrum SNR is superior to the DWFS SNR. However, for extended objects the power-spectrum SNR and the DWFS SNR are similar. Since speckle imaging uses a separate Fourier phasereconstruction process not required by the DWFS method, the DWFS method provides an alternative to speckle imaging that uses simple postprocessing at the cost of a wave-front sensor measurement but with no loss of SNR performance for extended objects.     

Reduced depth of field in incoherent hybrid imaging systems

A hybrid imaging system combines a modified optical imaging module and a digital postprocessing step. We define what to our knowledge is a new metric to quantify the blurring of a defocused image that is more suitable than the defocus parameter for describing defocused hybrid imaging systems. We use this metric to design a pupil phase grating to reduce the depth of field, thereby increasing the axial resolution, of an incoherent hybrid imaging system using quasi-monochromatic illumination. By introducing this grating at the exit pupil and digitally processing the output of the detector, we reduce the depth of field by more than a factor of 2. Finally, we examine the effect of using a CCD optical detector, instead of an ideal optical detector, on the reduction of the depth of field.     

Adaptive feature-specific imaging: a face recognition example

We present an adaptive feature-specific imaging (AFSI) system and consider its application to a face recognition task. The proposed system makes use of previous measurements to adapt the projection basis at each step. Using sequential hypothesis testing, we compare AFSI with static-FSI (SFSI) and static or adaptive conventional imaging in terms of the number of measurements required to achieve a specified probability of misclassification (Pe). The AFSI system exhibits significant improvement compared to SFSI and conventional imaging at low signal-to-noise ratio (SNR). It is shown that for M=4 hypotheses and desired Pe=10(-2), AFSI requires 100 times fewer measurements than the adaptive conventional imager at SNR= -20 dB. We also show a trade-off, in terms of average detection time, between measurement SNR and adaptation advantage, resulting in an optimal value of integration time (equivalent to SNR) per measurement.