The van Trees inequality relates the ensemble mean squared error of an estimator to a Bayesian version of the Fisher information. The Ziv-Zakai inequality relates the ensemble mean squared error of an estimator to the minimum probability of error for the task of detecting a change in the parameter. In this work we complete this circle by deriving an inequality that relates this minimum probability of error to the Bayesian version of the Fisher information. We discuss this result for both scalar and vector parameters. In the process we discover that an important intermediary in the calculation is the total variation of the posterior probability distribution function for the parameter given the data. This total variation is of interest in its own right since it may be easier to compute than the other figures of merit discussed here.We investigate photoacoustic (PA) signal magnitude variation to an absorption coefficient of localized absorbing objects measured by spherically focused ultrasound transducers (US TDs). For this investigation, we develop the PA simulation method that directly calculates Green function solutions of the Helmholtz PA wave equation, considering grid-like elements on absorbing objects and US TDs. The simulation results show that the PA signal amplitude in the PA imaging is nonlinearly varied to the absorption coefficient of localized objects, which are distinct from the known PA saturation effect. For spherical objects especially, the PA amplitude shows a maximum value at a certain absorption coefficient, and decreases even though the absorption coefficient further increases from that point. We suggest conceptual and mathematical interpretations for this phenomenon by analyzing the characteristics of PA spectra combined with US TD transfer functions, which indicates that the combined effect of US TD spatial and temporal filtering plays a significant role in the PA signal magnitude nonlinearity.Image scanning microscopy is a technique based on confocal microscopy, in which the confocal pinhole is replaced by a detector array, and the resulting image is reconstructed, usually by the process of pixel reassignment. The detector array collects most of the fluorescent light, so the signal-to-noise ratio is much improved compared with confocal microscopy with a small pinhole, while the resolution is improved compared with conventional (wide-field) microscopy. In previous studies, it has usually been assumed that pixels should be reassigned by a constant factor, to a point midway between the illumination and detection spots. Here it is shown that the peak intensity of the effective point spread function (PSF) can be further increased by 4% by a new choice of the pixel reassignment factor. For an array of two Airy units, the peak of the effective PSF is 1.90 times that of a conventional microscope, and the transverse resolution is 1.53 times better. It is confirmed that image scanning microscopy gives optical sectioning strength identical to that of a confocal microscope with a pinhole equal to the size of the detector array. However, it is shown that image scanning microscopy exhibits axial resolution superior to a confocal microscope with a pinhole the same size as the detector array. For a two-Airy-unit array, the axial resolution is 1.34 times better than in a conventional microscope for the standard reassignment factor, and 1.28 times better for the new reassignment factor. The axial resolution of a confocal microscope with a two-Airy-unit pinhole is only 1.04 times better than conventional microscopy. We also examine the signal-to-noise ratio of a point object in a uniform background (called the detectability), and show that it is 1.6 times higher than in a confocal microscope.We derive the analytic formula of the output surface of a spherochromatic lens. The analytic solution ensures that all the rays for a wide range of wavelengths fall inside the Airy disk. So, its amount of spherical aberration is small enough to consider the lens as diffracted limited. We test the singlet lens using ray-tracing methods and find satisfactory results, including spot diagram analysis for three different Abbe wavelengths.We derive the analytical formula of the energy weight of each orbital angular momentum (OAM) mode of twisted Gaussian Schell-model (TGSM) beams propagating in weak turbulent atmosphere. The evolution of its OAM spectrum is studied by numerical calculation. Our results show that the OAM spectrum of a TGSM beam changes with the beam propagating in turbulent atmosphere, which is completely different from that of the TGSM beam propagating in free space. Furthermore, influences of the source parameters and the turbulence parameters on the OAM spectrum of a TGSM beam in turbulent atmosphere are analyzed. It is found that the source parameters and turbulence parameters, such as twist factor, coherence length, beam waist size, and structure constant, have a significant influence on the OAM spectrum, but the value of the wavelength and inner scale have little influence. Increasing the beam waist size or decreasing the coherence length would lead to the OAM spectrum broadened in the source plane, but would be robust for the OAM modes of the TGSM beam in the turbulent atmosphere. It is clear that the bigger the value of the twist factor, the more asymmetric the OAM mode of the TGSM beam is, and the better mode distribution can be maintained when it propagates in turbulent atmosphere. Our results have potential applications in reducing the error rate of free-space optical communication and detecting the atmospheric parameters.Quantum random walks (QRWs) are random processes in which the resulting probability density of the „walker” state, whose movement is governed by a „coin” state, is described in a nonclassical manner. Previously, Q-plates have been used to demonstrate QRWs with polarization and orbital angular momentum playing the roles of coin and walker states, respectively. In this theoretical analysis, we show how stress-engineered optics can be used to develop new platforms for complex QRWs through relatively simple optical elements. Our work opens up new paths to speed up classical-to-quantum transitions in robust photonic networks.We discuss new effects related to relativistic aberration, which is the apparent distortion of objects moving at relativistic speeds relative to an idealized camera. Our analysis assumes that the camera lens is capable of stigmatic imaging of objects at rest with respect to the camera, and that each point on the shutter surface is transparent for one instant, but different points are not necessarily transparent synchronously. We pay special attention to the placement of the shutter. First, we find that a wide aperture requires the shutter to be placed in the detector plane to enable stigmatic images. Second, a Lorentz-transformation window [Proc. SPIE9193, 91931K (2014)PSISDG0277-786X10.1117/12.2061415] can correct for relativistic distortion. We illustrate our results, which are significant for future spaceships, with raytracing simulations.Wide generalizability of the CIE-recommended gray-scale calculation for self-luminous devices suggests that its parameters, the extrema of the calculation’s derivatives, and its limiting behavior are fundamental. The calculation has a negative-contrast point of inflection that is not predicted by any other gray-scale calculation, but that is consistent with data and with the terrestrial luminance histogram. The parameters of the calculation are analyzed, and their significance is explained. High-positive-contrast behavior of the calculation is shown and related to scientific literature. This knowledge represents a clearer understanding of daylight suprathreshold vision, and it enables optimal luminance-coding of contemporary high-resolution, high-contrast, high-luminance displays.Many applications of ultrashort laser pulses require manipulation and control of the pulse parameters by propagating them through different optical components before the target. This requires methods of simulating the pulse propagation taking into account all effects of dispersion, diffraction, and system aberrations. In this paper, we propose a method of propagating ultrashort pulses through a real optical system by using the Gaussian pulsed beam decomposition. An input pulse with arbitrary spatial and temporal (spectral) profiles is decomposed into a set of elementary Gaussian pulsed beams in the spatiospectral domain. The final scalar electric field of the ultrashort pulse after propagation is then obtained by performing the phase correct superposition of the electric fields all-Gaussian pulsed beams, which are propagated independently through the optical system. We demonstrate the application of the method by propagating an ultrashort pulse through a focusing aspherical lens with large chromatic aberration and a Bessel-X pulse generating axicon lens.Retinal image light distributions in a standard optical model of a diffraction-limited eye with round pupils are presented for several patterns of amplitude and phase modulation of the light admitted into the eye. Of special interest are circularly symmetrical configurations of truncated Bessel amplitude transmission functions, and of light subjected to axicon deviation. It is shown by several examples that this kind of beam shaping allows generation of retinal imagery, which can be more robust to defocus while maintaining minimal image degradation, and it points to situations of two separate zones simultaneously in sharp focus, several diopters apart.We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.We report on the generation of a hollow Bessel beam with a hole along the direction of propagation by using an easy-to-implement phase mask and investigate its effectiveness to reduce the out-of-focus background in light-sheet fluorescence microscopy (LSFM) with scanned Bessel beams by subtraction imaging. Overlaying $\pi $π-phase retardation between the two equal parts of the Bessel beam across the entrance pupil of the objective lens, a hollow Bessel beam with zero intensity at the focal plane can be achieved. By optimizing the numerical aperture of the annular mask applied in the hollow Bessel beam, matched distributions of the ring system between the hollow Bessel beam and the conventional Bessel beam are achieved. By subtraction between the two LSFM images, the out-of-focus blur caused by the ring system of the Bessel beam can be significantly reduced. Comparison with conventional Bessel LSFM images exhibits a better sectioning capability and higher contrast.