Tag Archives: fft

MTF, PSF, Sharpness, spectral response

Minimalist ESF, LSF, MTF by Monotonic Regression

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Because the Slanted Edge Method of estimating the Spectral Frequency Response of a camera and lens is one of the more popular articles on this site, I have fielded variations on the following question many times over the past ten years:

How do you go from the intensity cloud  produced by the projection of a slanted edge captured in a raw file to a good estimate of the relevant Line Spread Function?

Figure 1.  Slanted edge captured in the raw data and projected to the edge normal.  The data noisy because of shot noise and PRNU.  How to estimate the underlying edge profile (orange line, the Edge Spread Function)?

So I decided to write down the answer that I have settled on.  It relies on monotone spline regression to obtain an Edge Spread Function (ESF) and then reuses the parameters of the regression to infer the relative regularized Line Spread Function (LSF) analytically in one go.

This front-loads all uncertainty to just the estimation of the ESF since the other steps on the way to the SFR become purely mechanical.  In addition the monotonicity constraint puts some guardrails around the curve, keeping it on the straight and narrow without further effort.

This minimalist, what-you-see-is-what-you-get approach gets around the usual need for signal conditioning such as binning, finite difference calculations and other filtering, with their drawbacks and compensations.  It has the potential to be further refined so consider it a hot-rod DIY kit.  Even so it is an intuitively direct implementation of the method and it provides strong validation for Frans van den Bergh’s open source MTF Mapper, the undisputed king in this space,[1] as it produces very similar results with raw slanted edge captures. Continue reading Minimalist ESF, LSF, MTF by Monotonic Regression →

Quantization, Sensors, Spatial Resolution

The Units of Discrete Fourier Transforms

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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 Pattern 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:

Airy Mesh and Intensity
Figure 1. Airy disc image I(x,y). Left, 1a, 3D representation, zoomed in. Right, 1b, as it would appear on the sensing plane (yes, the rings are there but you need to squint to see them).

Continue reading The Units of Discrete Fourier Transforms →

Optics, Sensors, Sharpness, Spatial Resolution

A Simple Model for Sharpness in Digital Cameras – Diffraction and Pixel Aperture

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Now that we know from the introductory article that the spatial frequency response of a typical perfect digital camera and lens (its Modulation Transfer Function) can be modeled simply as the product of the Fourier Transform of the Point Spread Function of the lens and pixel aperture, convolved with a Dirac delta grid at cycles-per-pixel pitch spacing

(1)   \begin{equation*} MTF_{Sys2D} = \left|\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} }\right|_{pu}\ast\ast\: \delta\widehat{\delta_{pitch}} \end{equation*}

we can take a closer look at each of those components (pu here indicating normalization to one at the origin).   I used Matlab to generate the examples below but you can easily do the same with a spreadsheet.   Continue reading A Simple Model for Sharpness in Digital Cameras – Diffraction and Pixel Aperture →