<p>I am trying to understand how to derive the effective gain in [electrons / ADU] when stacking N frame images in different (summed, averaged, or medianed) ways. I found the  effective gains for the three kinds of stacking methods on page 20 in <a href="https://iraf.net/irafdocs/daorefman.pdf" rel="nofollow noreferrer">IRAF/DAOPHOT user's manual</a>.</p>
<ol>
<li><p>The image is the sum of N frames:
<strong>effective gain = gain</strong></p>
</li>
<li><p>The image is the average of N frames: <strong>effective gain = N * gain</strong></p>
</li>
<li><p>The image is the median of N frames: <strong>effective gain = 2.0 * N * gain / 3</strong></p>
</li>
</ol>
<p>To calculate photometry errors, I need to take these effective gains into consideration.
I would appreciate if you explain how to derive these results. Thank you.</p>

CC BY-SA 4.0
2023-03-03T18:30:10.123Z
I believe the last one must be some kind of approximation. The median of N frames should approach the average when $N$ is large. Please can you point to a page number in the document your referenced.
ProfRob
CC BY-SA 4.0
2023-03-04T01:38:17.733Z
@ProfRob Thank you for your comment. I see, it seems the result of median stacking is somewhat tricky. It says on the page 20 (I added it to the main text).
cosmozaka46
<observational-astronomy><photometry><image-processing><ccd>
Effective gain when stacking N frame images
cosmozaka46
# Effective gain when stacking N frame images

(Asked by: username_0 on 2023-03-03)

I am trying to understand how to derive the effective gain in [electrons / ADU] when stacking N frame images in different (summed, averaged, or medianed) ways. I found the effective gains for the three kinds of stacking methods on page 20 in [IRAF/DAOPHOT user's manual](https://iraf.net/irafdocs/daorefman.pdf).

1. The image is the sum of N frames:
   **effective gain = gain**
2. The image is the average of N frames: **effective gain = N \* gain**
3. The image is the median of N frames: **effective gain = 2.0 \* N \* gain / 3**

To calculate photometry errors, I need to take these effective gains into consideration.
I would appreciate if you explain how to derive these results. Thank you.

**Tags:** observational-astronomy, photometry, image-processing, ccd
> **Comments:**
> **username_1**: I believe the last one must be some kind of approximation. The median of N frames should approach the average when $N$ is large. Please can you point to a page number in the document your referenced.  
> **username_0**: @ProfRob Thank you for your comment. I see, it seems the result of median stacking is somewhat tricky. It says on the page 20 (I added it to the main text).  

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## 0 answers

