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 is about specifying the units of the Discrete Fourier Transform of an image and the various ways that they can be expressed. This apparently simple task can be fiendishly unintuitive.
The image we will use as an example is the familiar Airy Disk from the last few posts, at f/16 with light of mean 530nm wavelength. Zoomed in to the left in Figure 1; and as it looks in its 1024×1024 sample image to the right:
Now that we know from the introductory article that the spatial frequency response of a typical perfect digital camera and lens can be modeled simply as the product of the Modulation Transfer Function of the lens and pixel area, convolved with a Dirac delta grid at cycles-per-pixel spacing
The next few posts will describe a linear spatial resolution model that can help a photographer better understand the main variables involved in evaluating the ‘sharpness’ of photographic equipment and related captures. I will show numerically that the combined spectral frequency response (MTF) of a perfect AAless monochrome digital camera and lens in two dimensions can be described as the normalized multiplication of the Fourier Transform (FT) of the lens Point Spread Function by the FT of the (square) pixel footprint, convolved with the FT of a rectangular grid of Dirac delta functions centered at each pixel, as better described in the article
With a few simplifying assumptions we will see that the effect of the lens and sensor on the spatial resolution of the continuous image on the sensing plane can be broken down into these simple components. The overall ‘sharpness’ of the captured digital image can then be estimated by combining the ‘sharpness’ of each of them. Continue reading A Simple Model for Sharpness in Digital Cameras – I→
Equivalence – as we’ve discussed one of the fairest ways to compare the performance of two cameras of different physical formats, characteristics and specifications – essentially boils down to two simple realizations for digital photographers:
metrics need to be expressed in units of picture height (or diagonal where the aspect ratio is significantly different) in order to easily compare performance with images displayed at the same size; and
focal length changes proportionally to sensor size in order to capture identical scene content on a given sensor, all other things being equal.
The first realization should be intuitive (future post). The second one is the subject of this post: I will deal with it through a couple of geometrical diagrams.