This post will continue looking at the spatial frequency response measured by MTF Mapper off slanted edges in DPReview.com raw captures and relative fits by the ‘sharpness’ model discussed in the last few articles. The model takes the physical parameters of the digital camera and lens as inputs and produces theoretical directional system MTF curves comparable to measured data. As we will see the model seems to be able to simulate these systems well – at least within this limited set of parameters.
The following fits refer to the green channel of a number of interchangeable lens digital camera systems with different lenses, pixel sizes and formats – from the current Medium Format 100MP champ to the 1/2.3″ 18MP sensor size also sometimes found in the best smartphones. Here is the roster with the cameras as set up:
The series of articles starting here outlines a model of how the various physical components of a digital camera and lens can affect the ‘sharpness’ – that is the spatial resolution – of the images captured in the raw data. In this one we will pit the model against MTF curves obtained through the slanted edge methodfrom real world raw captures both with and without an anti-aliasing filter.
With a few simplifying assumptions, which include ignoring aliasing and phase, the spatial frequency response (SFR or MTF) of a photographic digital imaging system near the center can be expressed as the product of the Modulation Transfer Function of each component in it. For a current digital camera these would typically be the main ones:
We now know how to calculate the two dimensional Modulation Transfer Function of a perfect lens affected by diffraction, defocus and third order Spherical Aberration – under monochromatic light at the given wavelength and f-number. In digital photography however we almost never deal with light of a single wavelength. So what effect does an illuminant with a wide spectral power distribution, going through the color filter of a typical digital camera CFA before the sensor have on the spatial frequency responses discussed thus far?
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. The filter typically sits right on top of the sensing plane and its objective is to block as much of the aliasing and moiré creating energy above the Nyquist spatial frequency while letting through as much as possible of the real image forming energy below that, hence the low-pass designation.
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:
Having shown that our simple two dimensional MTF model is able to predict the performance of the combination of a perfect lens and square monochrome pixel we now turn to the effect of the sampling interval on spatial resolution according to the guiding formula:
The hats in this case mean the Fourier Transform of the relative component normalized to 1 at the origin (), that is the individual MTFs of the perfect lens PSF, the perfect square pixel and the delta grid.
Sampling in the Spatial and Frequency Domains
Sampling is expressed mathematically as a Kronecker delta function at the center of each pixel (the red dots below).
We’ve seen how to model sensors and how to collect signal and noise statistics from the raw data of our digital cameras. In this post I am going to pull both things together allowing us to estimate sensor IQ metrics: input-referred read noise, clipping/saturation/Full Well Count, Dynamic Range, Pixel Response Non-Uniformities and gain/sensitivity.
There are several ways to extract these metrics from signal and noise data obtained from a camera’s raw file. I will show two related ones: via SNR in this post and via total noise N in the next. The procedure is similar and the results are identical.