Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.

Background:The hallmark of gout is hyperuricemia. This substance has ties to cardiovascular disease's pathophysiology, which is the main killer of dialysis patients. Diabetes, insulin resistance, and other cardiovascular diseases as well as hypertension are all linked to hyperuricemia. Death from any cause is prevented by high SUA levels. Smaller studies found Jshaped relationships between SUA and all-cause mortality. In line with its function in protein metabolism, a recent study suggests that SUA could be used as a nutritional status indicator in hemodialysis patients. Rather than a high SUA, a superior nutritional state may explain survival connections. In HD patients, LVH with diverse etiologies is predictive of CV mortality and morbidity. Aim: to investigate the relationship between left ventricular morphological and functional problems and preand post-dialysis uric acid differences in individuals receiving maintenance hemodialysis. Subject and Methods: This study was carried out on ESRD patients in Internal Medicine Department of Benha University in the hemodialysis unit, where 100 patients were selected. Results: There were high statistically significant differences between the studied patients systolic and diastolic blood pressure before and after hemodialysis. There were high statistically significant differences between the studied patient's serum level of uric acid, creatinine and urea before and after hemodialysis. Conclusion: This study found a strong relationship between uric acid and both LV parameters and ejection fraction. We discovered through regression analysis that serum uric acid was an important indicator of LV ejection fraction.