Tag Archives: aliasing

Taking the Sharpness Model for a Spin – II

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:

Table 1. The cameras and lenses under test.

Continue reading Taking the Sharpness Model for a Spin – II

A Simple Model for Sharpness in Digital Cameras – AA

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[1].  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.

Downsizing Box 4X
Figure 1. The blue line indicates the pass through performance of an ideal anti-aliasing filter presented with an Airy PSF (Original): pass all spatial frequencies below Nyquist (0.5 c/p) and none above that. No filter has such ideal characteristics and if it did its hard edges would result in undesirable ringing in the image.

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:

Figure 2. Typical Optical Low Pass Filter implementation  in a current Digital Camera, courtesy of Nikon USA (yellow displacement ‘d’ added).

Continue reading A Simple Model for Sharpness in Digital Cameras – AA

A Simple Model for Sharpness in Digital Cameras – Aliasing

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:

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

The hats in this case mean the Fourier Transform of the relative component normalized to 1 at the origin (_{pu}), 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).

Figure 1. Left, 1a: A highly zoomed (3200%) image of the lens PSF, an Airy pattern, projected onto the imaging plane where the sensor sits. Pixels shown outlined in yellow. A red dot marks the sampling coordinates. Right, 1b: The sampled image zoomed at 16000%, 5x as much, because each pixel’s width is 5 linear units on the side.

Continue reading A Simple Model for Sharpness in Digital Cameras – Aliasing

A Simple Model for Sharpness in Digital Cameras – I

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

    \[ MTF_{2D} = \left|(\widehat{ PSF_{lens} }\cdot \widehat{PIX_{ap} })\ast\ast\: \delta\widehat{\delta_{pitch}}\right|_{pu} \]

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

The Slanted Edge Method

My preferred method for measuring the spatial resolution performance of photographic equipment these days is the slanted edge method.  It requires a minimum amount of additional effort compared to capturing and simply eye-balling a pinch, Siemens or other chart but it gives immensely more, useful, accurate, absolute information in the language and units that have been used to characterize optical systems for over a century: it produces a good approximation to  the Modulation Transfer Function of the two dimensional Point Spread Function of the camera/lens system in the direction perpendicular to the edge.

Much of what there is to know about a system’s spatial resolution performance can be deduced by analyzing such a curve, starting from the perceptually relevant MTF50 metric, discussed a while back.  And all of this simply from capturing the image of a black and white slanted edge, which one can easily produce and print at home.

Continue reading The Slanted Edge Method