Tag Archives: lp/ph

Taking the Sharpness Model for a Spin

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 method[1] from 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:

(1)   \begin{equation*} MTF_{sys} = MTF_{lens} (\cdot MTF_{AA}) \cdot MTF_{pixel} \end{equation*}

all in two dimensions Continue reading Taking the Sharpness Model for a Spin

The Units of Discrete Fourier Transforms

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:

Airy Mesh and Intensity
Figure 1. Airy disc image. Left, 1a, 3D representation, zoomed in. Right, 1b, as it would appear on the sensing plane.

Continue reading The Units of Discrete Fourier Transforms

Equivalence in Pictures: Sharpness/Spatial Resolution

So, is it true that a Four Thirds lens needs to be about twice as ‘sharp’ as its Full Frame counterpart in order to be able to display an image of spatial resolution equivalent to the larger format’s?

It is, because of the simple geometry I will describe in this article.  In fact with a few provisos one can generalize and say that lenses from any smaller format need to be ‘sharper’ by the ratio of their sensor linear sizes in order to produce the same linear resolution on same-sized final images.

This is one of the reasons why Ansel Adams shot 4×5 and 8×10 – and I would too, were it not for logistical and pecuniary concerns.

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The Units of Spatial Resolution

Several sites perform spatial resolution ‘sharpness’ testing of imaging systems for photographers (i.e. ‘lens+digital camera’) and publish results online.  You can also measure your own equipment relatively easily to determine how sharp your hardware is.  However comparing results from site to site and to your own can be difficult and/or misleading, starting from the multiplicity of units used: cycles/pixel, line pairs/mm, line widths/picture height, line pairs/image height, cycles/picture height etc.

This post will address the units involved in spatial resolution measurement using as an example readings from the slanted edge method.

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