# Stray Light Calculations

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Background:

Calculations:

## Page Contents

This page provides a description of the fundamental calculations that Imatest uses to generate stray light metric images.

# Metric Image Calculations

At a high level, the measurement of stray light is very simple: normalize the digital numbers (DNs) of an image, while (optionally) masking out the image of the light source. At a deeper level, it is a four-step process of:

## Dark-Level Subtraction

(Optionally) subtract off the user-provided dark level.

$$\text{image [DN]} = \text{image [DN]}-\text{dark level [DN]}$$

## Clipping

Any image values less than the user-provided dark level are clipped to

$$\text{clipped image [DN]} = \text{max}\left(\text{image [DN]}, \text{clipping value[DN]}\right)$$

Where the clipping value should be:

## Normalization Factor Application

### Transmission

The transmission stray light metric image calculation takes the test image and divides it by a normalization factor.

$$\text{stray light metric image} = \frac{\text{clipped image [DN]}}{\text{normalization factor [DN]}}$$

With appropriate normalization factors, this is used to compute the Point Source Transmission (PST) [1] and Point Source Rejection Ratio (PSRR) [2] metrics.

For a “transmission” calculation, no stray light is indicated with a value of zero and the worst possible stray light is indicated with a value of one.

### Attenuation

The attenuation stray light metric image calculation takes a normalization factor and divides it by the test image.

$$\text{stray light metric image} = \frac{\text{normalization factor [DN]}}{\text{clipped image [DN]}}$$

With appropriate normalization factors, this is used to compute the flare attenuation metric proposed within IEEE-P2020 [3].

For an “attenuation” calculation, no stray light is indicated with a value of infinity, and the worst possible stray light is indicated with a value of one.

Note: zero is a valid image value (corresponding to no measurable stray light from the test configuration). When using the attenuation calculation, these zeross get transformed to infinity, which in turn, will reduce the meaningfulness of some summary metrics (e.g., mean, max). To compensate for this, it is recommended to clip the image values to one.

## Data Transforms

There are many data transforms that can be applied to produce the metric image.

 Name Transform Linear $$y=x$$ Log 10 $$y=\log_{10}(x)$$ dB Power $$y=10\cdot\log_{10}(x)$$ dB Voltage $$y=20\cdot\log_{10}(x)$$ Log 2 $$y=\log_{2}(x)$$ Natural Log $$y=\ln(x)$$

Note: If using any of the logarithmic data transforms (any but linear), it is recommended to clip the image values to one.

# References

[1] E. Fest. 2013. “Stray Light Analysis and Control”. SPIE Press. ISBN: 9780819493255. DOI: https://doi.org/10.1117/3.1000980.

[2] B. Bouce, et. al, 1974. “GUERAP II – USER’S GUIDE”. Perkin-Elmer Corporation. AD-784 874.

[3] IEEE-P2020 Automotive Image Quality Working Group. https://site.ieee.org/sagroups-2020/