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 Dirac delta function at the center of each pixel (the red dots below).
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→
A number of interesting insights come to light once one realizes that as far as the slanted edge method (of measuring the Modulation Transfer Function of a Bayer CFA digital camera and lens from its raw data) is concerned it is as if it were dealing with identical full resolution images behind three color filters, each in their own separate color planes:
For the purposes of ‘sharpness’ spatial resolution measurement in photography cameras can be considered shift-invariant, linear systems.
Shift invariant means that the imaging system should respond exactly the same way no matter where light from the scene falls on the sensing medium . We know that in a strict sense this is not true because for instance a pixel has a square area so it cannot have an isotropic response by definition. However when using the slanted edge method of linear spatial resolution measurement we can effectively make it shift invariant by careful preparation of the testing setup. For example the edges should be slanted no more than this and no less than that. Continue reading Linearity in the Frequency Domain→
We know that the best Information Quality possible collected from the scene by a digital camera is available right at the output of the sensor and it will only be degraded from there. This article will discuss what happens to this information as it is transferred through the imaging system and stored in the raw data. It will use the simple language outlined in the last post to explain how and why the strategy for Capturing the best Information or Image Quality (IQ) possible from the scene in the raw data involves only two simple steps:
1) Maximizing the collected Signal given artistic and technical constraints; and
2) Choosing what part of the Signal to store in the raw data and what part to leave behind.
The second step is only necessary if your camera is incapable of storing the entire Signal at once (that is it is not ISO invariant) and will be discussed in a future article. In this post we will assume an ISOless imaging system.
Determining the Signal to Noise Ratio (SNR) curves of your digital camera at various ISOs and extracting from them the underlying IQ metrics of its sensor can help answer a number of questions useful to photography. For instance whether/when to raise ISO; what its dynamic range is; how noisy its output could be in various conditions; or how well it is likely to perform compared to other Digital Still Cameras. As it turns out obtaining the relative data is a little time consuming but not that hard. All you need is your camera, a suitable target, a neutral density filter, dcraw and free ImageJ, Octave or (pay) Matlab.