<p>In excitement regarding the JWST release, I came across <a href="https://trs.jpl.nasa.gov/bitstream/handle/2014/44677/09-3010_A1b.pdf" rel="nofollow noreferrer"><em>Krist et al, The JWST/NIRCam coronagraph: mask design and fabrication</em></a>, within which there is the following plot:</p>
<p><a href="https://i.sstatic.net/10NAL.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/10NAL.jpg" alt="Fig. 9. Focal plane images from the IRCT in K band (λ = 2.2
µm), **displayed as the quarter-root of intensity. DOI:10.1117/12.826448" /></a></p>
<blockquote>
<p>Fig. 9. Focal plane images from the IRCT in K band (λ = 2.2
µm), <strong>displayed as the quarter-root of intensity.</strong> (Left)
Image with a circular Lyot stop in place but no occulter.
(Right) Image with the 2.2 µm dot pattern mask and
Lyot stop in place, multiplied by 10000 in intensity to
compare with the image on the left. The speckles are due
to aberrations in the testbed.</p>
</blockquote>
<p>I'm curious if there is a physical rationale for why a quarter-root scaling would have been chosen? This paper is the only search result for &quot;quarter root of intensity&quot;, so was it simply an arbitrary decision to draw the eye, or does it have some basis in astronomy?</p>

CC BY-SA 4.0
2022-07-12T12:13:13.527Z
It's common to scale fluxes in images not linearly, but logarithmically or, less often (I think) as the square root. Other scalings are also sometimes used. This is to enhance low-luminosity regions. So my guess is that the answer is "The rationale is that this particular scaling enhanced best what the author wanted to enhance."
pela
CC BY-SA 4.0
2022-07-12T21:36:39.953Z
Good question! I have seen square root of intensity in another JWST engineering image, and the rational for that *might be* that it's the absolute value of amplitude. Fourth root would just make the dimmer bits brighter so more blobs are more easily visible. I have a hunch there will be no profound explanation beyond that.
uhoh
CC BY-SA 4.0
2022-07-12T22:03:12.537Z
In section 2.1 of the paper, there are two functions for intensity, both of which are 4th degree polynomials.
DavePhD
CC BY-SA 4.0
2022-07-13T12:13:16.780Z
If by "quarter-root" you mean $x^{\frac{1}{4}}$  , then that's equivalent to the square rooot of amplitude.  Maybe that's of interest in some analysis or equations related to this  situation?    Then again,  I think @uhoh is on the right track:  scaling an image by a root, or even log(intensity) often makes it much easier to see low-intensity features without clipping the brightest regions.
Carl Witthoft
<james-webb-space-telescope><image-processing><post-processing><coronograph>
"Quarter root of intensity" in coronographic plots
0xDBFB7
# "Quarter root of intensity" in coronographic plots

(Asked by: username_0 on 2022-07-12)

In excitement regarding the JWST release, I came across [*Krist et al, The JWST/NIRCam coronagraph: mask design and fabrication*](https://trs.jpl.nasa.gov/bitstream/handle/2014/44677/09-3010_A1b.pdf), within which there is the following plot:

[![Fig. 9. Focal plane images from the IRCT in K band (λ = 2.2
µm), **displayed as the quarter-root of intensity. DOI:10.1117/12.826448](https://i.sstatic.net/10NAL.jpg)](https://i.sstatic.net/10NAL.jpg)

> Fig. 9. Focal plane images from the IRCT in K band (λ = 2.2
> µm), **displayed as the quarter-root of intensity.** (Left)
> Image with a circular Lyot stop in place but no occulter.
> (Right) Image with the 2.2 µm dot pattern mask and
> Lyot stop in place, multiplied by 10000 in intensity to
> compare with the image on the left. The speckles are due
> to aberrations in the testbed.

I'm curious if there is a physical rationale for why a quarter-root scaling would have been chosen? This paper is the only search result for "quarter root of intensity", so was it simply an arbitrary decision to draw the eye, or does it have some basis in astronomy?

**Tags:** james-webb-space-telescope, image-processing, post-processing, coronograph

> **Comments:**
> **username_1**: It's common to scale fluxes in images not linearly, but logarithmically or, less often (I think) as the square root. Other scalings are also sometimes used. This is to enhance low-luminosity regions. So my guess is that the answer is "The rationale is that this particular scaling enhanced best what the author wanted to enhance."  
> **username_2**: Good question! I have seen square root of intensity in another JWST engineering image, and the rational for that *might be* that it's the absolute value of amplitude. Fourth root would just make the dimmer bits brighter so more blobs are more easily visible. I have a hunch there will be no profound explanation beyond that.  
> **username_3**: In section 2.1 of the paper, there are two functions for intensity, both of which are 4th degree polynomials.  
> **username_4**: If by "quarter-root" you mean $x^{\frac{1}{4}}$  , then that's equivalent to the square rooot of amplitude.  Maybe that's of interest in some analysis or equations related to this  situation?    Then again,  I think @username_2 is on the right track:  scaling an image by a root, or even log(intensity) often makes it much easier to see low-intensity features without clipping the brightest regions.  

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## 0 answers

