Calculation of the modulation transfer function for object brightness distribution function oriented along any direction in axis-symmetrical optical systems

Abstract

The literature deals with the modulation transfer function (MTF) only for object brightness distribution functions (OBDFs) oriented along the meridional and sagittal directions. This paper addresses computation of the geometrical MTF for an off-axis source point when the OBDF is oriented along any arbitrarily defined direction. This study finds that the MTF is not a monotonic increasing or decreasing function when the direction of the OBDF is changing. Consequently, the extreme MTF values may occur when the OBDF is aligned at any direction between the meridional and sagittal directions. Four theorems are provided for the MTF and the phase shift variations that take place when the OBDF is translated or rotated. It is found that the MTF and the phase shift are symmetrical or antisymmetrical about certain directions. Thus, to observe all possible changes in the MTF and the phase shift, it is sufficient to rotate the OBDF through a range of just 90°. The presented method is based on a recent irradiance method for MTF computation that does not rely on counting the number of ray hits on a mesh, making the method immune to effects of grid size and thus improving traditional accuracy.

Impact of the optical depth of field on cytogenetic image quality

“…24 Second, a simple DOF measurement was used and we did not test whether applying the new contrast calculation methods proposed recently could achieve more accurate results. [25][26][27][28][29] Third, although the DOF of the human eye is also an important factor affecting subjective evaluation of the cytogenetic image qualities, 30,31 it was not tested or discussed. Hence, a more comprehensive investigation is underway from which we hope to acquire better knowledge about the designing trade-off parameters to optimize the automated digital microscopic image scanning systems for cytogenetic image diagnosis and other digital pathology applications in the future.…”

Statistic estimation and validation of in-orbit modulation transfer function based on fractal characteristics of remote sensing images

“…One method is based on fixed characteristic targets including the sine-wave method, spots, slits and edge method [4][5][6]. The other method is based on random targets [7].…”

Measurement of the optical transfer function using a white-dot pattern presented on a liquid-crystal display

“…They can be determined either from scalar wave theory or from geometrical optics. These two approaches are generally referred to as the diffractive MTF and the geometric MTF respectively [4]. Any MTF quantifies the system's capacity to spatially resolve a sinusoidal intensity pattern with discernible contrast [4,7].…”

“…These two approaches are generally referred to as the diffractive MTF and the geometric MTF respectively [4]. Any MTF quantifies the system's capacity to spatially resolve a sinusoidal intensity pattern with discernible contrast [4,7]. Previous studies have proposed several methods for measuring the MTF of optical systems based on detector arrays of charge-coupled devices (CCDs) [8] and most of them differ essentially in the type of target or pattern used as the object pattern [9].…”

“…Previous studies have proposed several methods for measuring the MTF of optical systems based on detector arrays of charge-coupled devices (CCDs) [8] and most of them differ essentially in the type of target or pattern used as the object pattern [9]. These techniques can be broadly classified into five categories: the sine-wave method, the bar-target method, the edge-gradient method, the series-expansion method and the random-pattern method [4]. According to the sine-wave method a target object with a sine-wave variation in intensity is imaged and the MTF is taken to be the ratio of the image-to-object modulation depth.…”