Analytical expression for the average ensquared energy

Abstract

We derive an expression for the average area of intersection between a blur spot of radius R and a square pixel, where the center of the blur is uniformly chosen from the pixel interior. Implications of the result are then discussed in the context of a point source detection problem.

Tuning the optical isotropic point of mixed crystals of ethylenediammonium sulfate/selenate

“…Recent developments in the field of Mueller matrix polarimetry, including polarimeter design (Arteaga et al, 2012), optical modeling (Nichols et al, 2017) and data fitting (Martin, 2018), have greatly improved our ability to measure dispersion in optical tensors of bianisotropic media. The partial wave method (Nichols et al, 2015) was employed here to calculate the Mueller matrix, a 4 Â 4 polarization transformation matrix that encodes all information related to the linear optical effects: LB, CB, linear dichroism (LD) and circular dichroism (CD). The partial wave method accounts for loss of coherence between multiple reflections or multiply reflected transmissions in ellipsometry and polarimetry, respectively.…”

“…Ethylenediammonium is a flexible cation that has been characterized in salts of more than 40 anions, many of which are isostructural and some of which are isomorphous with one another (Srinivasan et al, 2013). Recent research has employed Mueller matrix polarimetry with variable coherence optical models (Postava et al, 2002;Nichols et al, 2015;Martin et al, 2017b;Nichols, 2018;Arteaga & Kahr, 2019) to establish the linear birefringence (LB) and circular birefringence (CB) anisotropies in isomorphous crystals [space groups P4 1(3) 2 1 2] of ethylenediammonium sulfate (EDS) (Nichols et al, 2016) and ethylenediammonium selenate (EDSe) (Martin et al, 2017a). These isomorphs differ in the near-visible part of the electromagnetic spectrum in that EDSe exhibits an isotropic point, an accidental linear anisotropy compensation (Hobden, 1968a,b), and EDS does not.…”

Detection and recognition of a ground moving target under random dynamic conditions

“…The detection time is influenced by the flight altitude of carrier aircraft and the relative velocity between the ground moving target and the carrier aircraft, and it also determines the radiation energy received by the photoelectric detector. According to Formula (8), the curve of the radiation illumination received by the photoelectric detector, and the relative velocity between the ground moving target and the carrier aircraft is shown in Figure 5 under different wavelength conditions.…”

“…Besides, in the different flight attitudes of the carrier aircraft process, the spatial attitude angle of the airborne photoelectric detection device passively changes because of the influence of the varying pitch angle and azimuth angle of the carrier aircraft. Therefore, the rotation state of the airborne photoelectric detection system is affected by the rotation state of the photoelectric detection device itself and the flight attitude of the carrier aircraft 8,9 . To establish the detection model of ground moving target by the airborne photoelectric detection system under random dynamic conditions, the detection mechanism of the airborne photoelectric detection system for ground moving target is studied based on this detection principle, the radiation illumination characteristics model of the ground moving target under random dynamic condition is set up, the radiation energy of photoelectric detector is calculated, and the signal calculation function of the ground moving target is output, which gives the detection performance of the airborne photoelectric detection system under random dynamic condition and the recognition effect of the photoelectric detection system for the ground moving target can be analyzed.…”