transfer function | Strolls with my Dog

Texture MTF is a method to measure the sharpness of a digital camera and lens by capturing the image of a target of known characteristics. It purports to better evaluate the perception of fine details in low contrast areas of the image – what is referred to as ‘texture’ – in the presence of noise reduction, sharpening or other non-linear processing performed by the camera before writing data to file.

Figure 1. Image of Dead Leaves low contrast target. Such targets are designed to have controlled scale and direction invariant features with a power law Power Spectrum.

The Modulation Transfer Function (MTF) of an imaging system represents its spatial frequency response, from which many metrics related to perceived sharpness are derived: MTF50, SQF, SQRI, CMT Acutance etc. In these pages we have used to good effect the slanted edge method to obtain accurate estimates of a system’s MTF curves in the past.^[1]

In this article we will explore proposed methods to determine Texture MTF and/or estimate the Optical Transfer Function of the imaging system under test from a reference power-law Power Spectrum target. All three rely on variations of the ratio of captured to reference image in the frequency domain: straight Fourier Transforms; Power Spectral Density; and Cross Power Density. In so doing we will develop some intuitions about their strengths and weaknesses. Continue reading Introduction to Texture MTF →

This article will discuss a simple frequency domain model for an AntiAliasing (or Optical Low Pass) Filter, a hardware component sometimes found in a digital imaging system^[1]. The filter typically sits just above the sensor and its objective is to block as much of the aliasing and moiré creating energy above the monochrome Nyquist spatial frequency while letting through as much as possible of the real image forming energy below that, hence the low-pass designation.

Downsizing Box 4X — Figure 1. The blue line indicates the pass through performance of an ideal anti-aliasing filter presented with an Airy PSF (Original): pass all spatial frequencies below Nyquist (0.5 c/p) and none above that. No filter has such ideal characteristics and if it did its hard edges would result in undesirable ringing in the image.

In consumer digital cameras it is often implemented by introducing one or two birefringent plates in the sensor’s filter stack. This is how Nikon shows it for one of its DSLRs:

d800-aa1 — Figure 2. Typical Optical Low Pass Filter implementation in a current Digital Camera, courtesy of Nikon USA (yellow displacement ‘d’ added).

Continue reading A Simple Model for Sharpness in Digital Cameras – AA →

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