<p>TDI is aimed at enhancing signal-to-noise ratio (SNR) rather than contrast. The enhanced SNR is proportional to <span class="math-container">$N^{0.5}$</span>, where <span class="math-container">$N$</span> is the number of measurements on the same object.</p>
<p>Proof. Assuming noises are uncorrelated between two observations,
the variance of integrated signal-to-noise ratio (SNR) can be simplified as follows:</p>
<p><span class="math-container">$\displaystyle\sigma^2_{X+Y}=\sigma^2_{X}+\sigma^2_{Y}+2\text{Cov}(X,Y)=\sigma^2_{X}+\sigma^2_{Y}\sim2\sigma^2_{X}$</span>.</p>
<p>The integrated SNR turns out to be:</p>
<p><span class="math-container">$\displaystyle\frac{S_{X+Y}}{\sigma_{X+Y}}\sim\frac{S_{X}+S_{Y}}{2^{0.5}\sigma_{X}}=\left[\frac{(S_{X}+S_{Y})0.5}{\sigma_{X}}\right]2^{0.5}\sim\left(\frac{S_{X}}{\sigma_{X}}\right)2^{0.5}$</span>,</p>
<p>, which is higher than individual SNR by <span class="math-container">$2^{0.5}$</span>.</p>
<p>Similar conclusion can be drawn when measuring the same object <span class="math-container">$N$</span> times, the integrated SNR can be enhanced by a factor of <span class="math-container">$\sqrt{N}$</span>.</p>

CC BY-SA 4.0
2022-12-11T09:03:06.147Z
@uhoh Thanks for your great efforts on maintaining Stack Exchange! I have converted my answer to text/LaTex!
Rocky Tseng
CC BY-SA 4.0
2022-12-11T11:43:17.237Z
*Excellent, thanks!*
uhoh
CC BY-SA 4.0
2022-12-09T07:53:55.630Z
2022-12-12T13:08:47.697Z
2022-12-12T13:08:47.697Z
Rocky Tseng
<p>As shown in the figure below, the Time Delay Integration (TDI, the right side of the figure) is aimed at accumulating multiple exposures of the same (moving) object, effectively increasing the integration time available to collect incident light.</p>
<p>The question is, can we simply multiply a positive value to each pixel within a low-contrast image in order to enhance contrast and to discard TDI technique? (e.g. <a href="https://www.geeksforgeeks.org/opencv-understanding-contrast-in-an-image/#:%7E:text=To%20increase%20the%20contrast%20levels,each%20and%20every%20image%20pixel." rel="nofollow noreferrer">example</a>)</p>
<p>Someone may argue that pixels may have a risk at saturation after multiplying a contrast factor. Yes, but we can initially scale each pixel value down and multiply a contrast factor later to avoid the saturation issue. I am sure that I have missed something. I will appreciate it if you provide an answer, thanks!</p>
<p><a href="https://i.sstatic.net/HleUA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HleUA.png" alt="enter image description here" /></a></p>
<p>Why is this question relevant to astronomy? Strictly speaking, the question is relevant to Astrophotography. Please
refer to <a href="https://astronomy.stackexchange.com/q/44086/7982">What was the first use of time-delay integration in Astronomy? Are there instances before GAIA?</a></p>

CC BY-SA 4.0
2022-12-09T21:34:47.040Z
relevant https://astronomy.stackexchange.com/questions/44086/
James K
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2022-12-09T23:51:28.873Z
@JamesK Why did you think it was relevant?
Rocky Tseng
CC BY-SA 4.0
2022-12-10T03:29:09.793Z
@uhoh asked you to make the relevance to astronomy, for example describing how the technique is used in astrophotography.  That is a post about the use of TDI in astrophotography.  Hence it is relevant to how you could improve this question.
James K
CC BY-SA 4.0
2022-12-11T09:21:30.633Z
@uhoh, thanks for your reminder! I have put a short description into the post!
Rocky Tseng
CC BY-SA 4.0
2022-12-11T11:45:18.100Z
Looks great, *thanks!*
uhoh
CC BY-SA 4.0
2022-12-12T21:24:49.367Z
[Shall we at least temporarily ban chatbot-generated posting until it becomes clearer what it means for Stack Exchange?](https://astronomy.meta.stackexchange.com/q/890/7982)
uhoh
CC BY-SA 4.0
2022-12-20T21:16:16.653Z
@uhoh It appears my answer to your question has been added to the 
 Community Policy Repository: https://astronomy.meta.stackexchange.com/questions/560/community-policy-repository, so ChatGPT is temporarily banned on this site.  I am editing the above question accordingly.
Connor Garcia
CC BY-SA 4.0
2022-12-09T12:28:44.057Z
Multiplying by a constant value (as opposed to using a nonlinear function) won't even "enhance contrast", let alone increase signal-to-noise, which is what longer integrations (whether staring or TDI) do.
Peter Erwin
<observational-astronomy><photography>
Can we simply multiply a positive value to each pixel in order to enhance contrast and to discard Time Delay Integration technique?
Rocky Tseng
# Can we simply multiply a positive value to each pixel in order to enhance contrast and to discard Time Delay Integration technique?

(Asked by: username_0 on 2022-12-09)

As shown in the figure below, the Time Delay Integration (TDI, the right side of the figure) is aimed at accumulating multiple exposures of the same (moving) object, effectively increasing the integration time available to collect incident light.

The question is, can we simply multiply a positive value to each pixel within a low-contrast image in order to enhance contrast and to discard TDI technique? (e.g. [example](https://www.geeksforgeeks.org/opencv-understanding-contrast-in-an-image/#:%7E:text=To%20increase%20the%20contrast%20levels,each%20and%20every%20image%20pixel.))

Someone may argue that pixels may have a risk at saturation after multiplying a contrast factor. Yes, but we can initially scale each pixel value down and multiply a contrast factor later to avoid the saturation issue. I am sure that I have missed something. I will appreciate it if you provide an answer, thanks!

[![enter image description here](https://i.sstatic.net/HleUA.png)](https://i.sstatic.net/HleUA.png)

Why is this question relevant to astronomy? Strictly speaking, the question is relevant to Astrophotography. Please
refer to [What was the first use of time-delay integration in Astronomy? Are there instances before GAIA?](https://astronomy.stackexchange.com/q/44086/7982)

**Tags:** observational-astronomy, photography
> **Comments:**
> **username_4**: Multiplying by a constant value (as opposed to using a nonlinear function) won't even "enhance contrast", let alone increase signal-to-noise, which is what longer integrations (whether staring or TDI) do.  
> **username_1**: relevant https://astronomy.stackexchange.com/questions/44086/  
> **username_0**: @JamesK Why did you think it was relevant?  
> **username_1**: @uhoh asked you to make the relevance to astronomy, for example describing how the technique is used in astrophotography.  That is a post about the use of TDI in astrophotography.  Hence it is relevant to how you could improve this question.  
> **username_0**: @uhoh, thanks for your reminder! I have put a short description into the post!  
> **username_2**: Looks great, *thanks!*  
> **username_2**: [Shall we at least temporarily ban chatbot-generated posting until it becomes clearer what it means for Stack Exchange?](https://astronomy.meta.stackexchange.com/q/890/7982)  
> **username_3**: @uhoh It appears my answer to your question has been added to the   Community Policy Repository: https://astronomy.meta.stackexchange.com/questions/560/community-policy-repository, so ChatGPT is temporarily banned on this site.  I am editing the above question accordingly.  

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## 1 answers

### Answer by username_0 on 2022-12-09. Score: 4

TDI is aimed at enhancing signal-to-noise ratio (SNR) rather than contrast. The enhanced SNR is proportional to $N^{0.5}$, where $N$ is the number of measurements on the same object.

Proof. Assuming noises are uncorrelated between two observations,
the variance of integrated signal-to-noise ratio (SNR) can be simplified as follows:

$\displaystyle\sigma^2\_{X+Y}=\sigma^2\_{X}+\sigma^2\_{Y}+2\text{Cov}(X,Y)=\sigma^2\_{X}+\sigma^2\_{Y}\sim2\sigma^2\_{X}$.

The integrated SNR turns out to be:

$\displaystyle\frac{S\_{X+Y}}{\sigma\_{X+Y}}\sim\frac{S\_{X}+S\_{Y}}{2^{0.5}\sigma\_{X}}=\left[\frac{(S\_{X}+S\_{Y})0.5}{\sigma\_{X}}\right]2^{0.5}\sim\left(\frac{S\_{X}}{\sigma\_{X}}\right)2^{0.5}$,

, which is higher than individual SNR by $2^{0.5}$.

Similar conclusion can be drawn when measuring the same object $N$ times, the integrated SNR can be enhanced by a factor of $\sqrt{N}$.

> **Comments:**
> **username_0**: @uhoh Thanks for your great efforts on maintaining Stack Exchange! I have converted my answer to text/LaTex!  
> **username_2**: *Excellent, thanks!*  

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