Shalin B. Mehta

Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast

We describe a full-field phase-gradient imaging method: asymmetric illumination-based differential phase contrast (AIDPC). Imaging properties of AIDPC are evaluated using the phase-gradient transfer-function approach and elucidated with experimental images of an optical fiber and a histochemical preparation of a skeletal muscle section. In comparison with full-field differential interference contrast, AIDPC does not require phase shifting for quantitative imaging of phase gradient, provides artifact-free images of birefringent specimens, requires shorter camera exposure, and has larger depth of focus. It is amenable to transfer-function engineering, simultaneous fluorescence imaging, and automated live cell imaging.

Partially coherent image formation in differential interference contrast (DIC) microscope

Some different image formation models have been proposed for Nomarskis differential interference contrast (DIC) microscope. However, the nature of coherence of illumination in DIC, of key importance in image formation, remains to be elucidated. We present a partially coherent image formation model for DIC and demonstrate that DIC microscope images the coherent difference of shifted replicas of the specimen; but imaging of the each component is partially coherent. Partially coherent transfer functions are presented for various DIC configurations. Plots of these transfer functions and experimental images provide quantitative comparison among various DIC configurations and elucidate their imaging properties. Approximations for weak or slowly varying specimens are also given. These improved models should be of great value in designing phase retrieval algorithms for DIC.

Phase-space representation of partially coherent imaging systems using the Cohen class distribution

We develop a phase-space representation (termed phase-space imager) suitable for analysis and design of imaging systems that use large illumination apertures (partially coherent illumination). The representation, developed from the transmission cross-coefficient model, falls in the general Cohen class of distributions and elegantly captures the bilinear nature of image formation in partially coherent systems. It uses only the requisite number of dimensions and leads to an efficient algorithm for calculating images. Computed partially coherent images of a double slit and a two-dimensional sinusoidal spoke are presented.

Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement–coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimens phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

Sample-less calibration of the differential interference contrast microscope.

Analysis of image formation in a differential interference contrast (DIC) microscope and retrieval of the specimens properties require calibration of its key parameters, viz. shear and bias. We present a method of measuring the shear and the bias of a DIC microscope from the interference fringes produced in the back focal plane of the objective. Previous approaches, which use calibrated specimens such as polystyrene or fluorescent beads, provide rather approximate measurements of shear or require a complex optical setup. The method presented is accurate, relies on simple image analysis, and does not require a specimen. We provide a succinct and accurate description of properties of Nomarski prisms to explain the rationale behind the method.

Partially coherent microscope in phase space

Explicit expressions are presented for different phase-space representations (mutual intensity, Wigner distribution function, and ambiguity function) of the partially coherent image wave field in a microscope system. These are separated into system- and object-dependent parts. The partially coherent image in phase space can be described in terms of different 6D system-dependent kernels, all Fourier transforms of the system mutual spectrum, the region of overlap of two displaced objective pupils and the effective source. The image intensity can be expressed in terms of a 4D kernel, the convolution in spatial frequency of the source, and the Wigner distribution function of the objective pupil, given by a marginal of, or a section through, the respective phase-space kernels.

Transfer Function Analysis of Partially Coherent Phase Imaging Methods and Evaluation for Quantitative Imaging

We present transfer function based analysis of contrast generated by various partially coherent phase imaging methods with emphasis on quantitative nature of differential phase contrast (DPC) and differential interference contrast (DIC).

Partially coherent imaging in phase space

Conventional optical microscopes, such as brightfield, darkfield, phase contrast or differential interference contrast microscopes are partially coherent imaging systems. Imaging in a partially coherent system was first analyzed by Hopkins only in 1953. He propagated the mutual intensity through the optical system, but did not give an expression for the mutual intensity of the image itself. The mutual intensity is a four dimensional (4D) quantity that contains information about the modulus and phase of the image wave field, which depends on the object’s complex refractive index in 3D. The mutual intensity is related to other representations such as the Wigner distribution function (WDF) and ambiguity function. Explicit expressions for different phase space representations of the image wave field are given. The expressions separate into system and object dependent parts. In addition, explicit relationships between the defocused partially coherent cross-coefficient and phase space representations in the image plane are derived.

Image Formation and Analysis of Coherent Microscopy and Beyond - Toward Better Imaging and Phase Recovery

Applications of phase microscopy based on either coherent or partially coherent sources are widely distributed in todays biological and biomedical research laboratories. But the quantitative phase information derivable from these techniques is often not fully understood, because in general, no universal theoretical model can be set up, and each of the techniques has to be treated specifically. This chapter is dedicated to the fundamental understanding of the methodologies that derive optical phase information using imaging techniques and microscopic instrumentation. Several of the latest and most significant techniques are thoroughly studied through the theoretical formalism of the optical transfer function. In particular, we classify these systems into two main categories: those based on coherent illumination, such as digital holographic microscopy (DHM) and its extension into tomography, and those based on partially coherent illumination, such as differential interference contrast (DIC) and differential phase contrast (DPC). Our intention is that the models described in this chapter give an insight into the behaviour of these phase imaging techniques, so that better instrumentation can be designed and improved phase retrieval algorithms can be devised.

Partially coherent image formation in Asymmetric Illumination-based Differential Phase Contrast (AIDPC) and phase-retrieval

Differential phase contrast (DPC) was first proposed in scanning electron and optical microscopy to image gradient of the specimen’s optical path length. We introduced AIDPC as an oblique illumination‐based partially coherent imaging method which is a full‐field equivalent of the scanning DPC system. We described imaging with AIDPC assuming a slowly varying specimen. Recently, we have developed an accurate paraxial phase‐space model, termed phase‐space imager (PSI), for describing image formation in a general partially coherent system. In this paper, we use PSI to compute partially coherent images of a general 2D specimen. We also simulate phase‐retrieval process with AIDPC. These accurate simulated results, presented for the fist time, provide evaluation of the key steps involved in phase‐retrieval using AIDPC.