aperture diameter | Strolls with my Dog

In the last article we saw that the intensity Point Spread Function and the Modulation Transfer Function of a lens could be easily approximated numerically by applying Discrete Fourier Transforms to its generalized exit pupil function $\mathcal{P}$ twice in sequence.^[1]

Obtaining the 2D DFTs is easy: simply feed MxN numbers representing the two dimensional complex image of the Exit Pupil function in its $uv$ space to a Fast Fourier Transform routine and, presto, it produces MxN numbers representing the amplitude of the PSF on the $xy$ sensing plane. Figure 1a shows a simple case where pupil function $\mathcal{P}$ is a uniform disk representing the circular aperture of a perfect lens with MxN = 1024×1024. Figure 1b is the resulting intensity PSF.

Figure 1a, left: A circular array of ones appearing as a white disk on a black background, representing a circular aperture. Figure 1b, right: Array of numbers representing the PSF of image 1a in the classic shape of an Airy Pattern. — Figure 1. 1a Left: Array of numbers representing a circular aperture (zeros for black and ones for white). 1b Right: Array of numbers representing the PSF of image 1a (contrast slightly boosted).

Simple and fast. Wonderful. Below is a slice through the center, the 513th row, zoomed in. Hmm…. What are the physical units on the axes of displayed data produced by the DFT? Continue reading Wavefront to PSF to MTF: Physical Units →

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 (see next post). The second one is the subject of this post: I will deal with it through a couple of geometrical diagrams.

Continue reading Equivalence in Pictures: Focal Length, f-number, diffraction, DOF →

Musings about Photography