<p>This is a brief and very general answer which points to some papers which deal with LIGO calibration in detail. More detailed answers might be possibly given on either point, but can easily cover complete books each easily, too.</p>
<p>A response or <a href="https://en.wikipedia.org/wiki/Transfer_function" rel="nofollow noreferrer">transfer function</a> of a piece of equipment describes how the device responds to an input signal. This could be in terms of frequency, of photon efficiency, of spatial resolution / diffraction for an optical piece of equipment etc.</p>
<p>Mathematically the detected signal is the convolution of the original (unchanged) signal with the transfer function of the instrument. In order to obtain the original signal you have to know your transfer function and <a href="https://en.wikipedia.org/wiki/Deconvolution" rel="nofollow noreferrer">deconvolve</a> the detected signal with the (hopefully measured and thus well-known) transfer function of your instrument.</p>
<p>In the case of these detectors the most interesting behaviour is the wavelength (or frequency) dependency of the sensitivity of the detectors, thus how well or easily we can detect a signal with a given frequency - possibly as a function of the direction of the signal direction with respect to the sensor orientation.</p>
<p>On the detailed calibration, thus establishment of this particular instrument's transfer function is topic of various works which took years to measure and establish. Some relevant papers on this topic might be these which discuss the sensor calibration prior to measurements - establishment of the sensor's transfer function is essential part of this:</p>
<ul>
<li><a href="https://pure.mpg.de/rest/items/item_795570/component/file_1152583/content" rel="nofollow noreferrer">https://pure.mpg.de/rest/items/item_795570/component/file_1152583/content</a></li>
<li><a href="https://dcc.ligo.org/public/0122/P1500248/015/P1500248_EarlyaLIGOCalUncertainty.pdf" rel="nofollow noreferrer">https://dcc.ligo.org/public/0122/P1500248/015/P1500248_EarlyaLIGOCalUncertainty.pdf</a></li>
</ul>

CC BY-SA 4.0
2022-01-10T08:12:46.750Z
Thanks for answering this question, I was looking exactly the same thing as mentioned in the given papers.
Junaid Ihsan
CC BY-SA 4.0
2022-01-09T20:44:15.390Z
2022-01-09T20:54:28.727Z
2022-01-09T20:54:28.727Z
planetmaker
<p>&quot;Laser Interferometer Gravitational-wave Observatory&quot; (LIGO) is a marvel of precise engineering and the world's largest gravitational wave observatory. LIGO, which consists of two massive laser interferometers separated by 3000 kilometers, uses the physical characteristics of light and space to detect and explain the sources of gravitational waves (GW).  <a href="https://www.ligo.caltech.edu/page/what-is-ligo" rel="nofollow noreferrer">https://www.ligo.caltech.edu/page/what-is-ligo</a></p>
<p><strong>1. What is mean by response or transfer function and what is LIGO  detector's response function?</strong> <em>(Mathematical Explanation will be preferred)</em></p>

CC BY-SA 4.0
2022-01-09T13:08:16.677Z
A search for "LIGO  detector response function" gives a plethora of scientific papers which deal with the calibration of the LIGO detectors. What exactly are you looking for at what level?

Also you seem to quote a text without giving source of it. Please link the source you quote.
planetmaker
CC BY-SA 4.0
2022-01-09T16:06:03.790Z
@planetmaker I added the source, I'm looking for some mathematical concept behind this response function? What mathematical functions are used ?
Junaid Ihsan
CC BY-SA 4.0
2022-01-09T16:59:56.353Z
Do you know what a response or transfer function is in physics for a detector? Or are you asking about the details for this particular instrument? Your question is quite unclear on this... What is your prior knowledge on this matter? Please elaborate :)
planetmaker
CC BY-SA 4.0
2022-01-09T19:43:18.387Z
@planetmaker kindly see my edited question.
Junaid Ihsan
CC BY-SA 4.0
2022-01-09T20:23:50.360Z
@JunaidIhsan in order to write an answer that is helpful, it helps to explain how much you are or are not familiar with the concept of a [transfer function](https://en.wikipedia.org/wiki/Transfer_function) in general. It could take a full chapter of a book to cover everything that *might* cover LIGO's transfer function alone, and that's too much, and after writing a long answer, you might comment "No, that's not what I want to know" or "I know that already" so folks may just not post anything. There are whole books and semester courses on transfer functions!
uhoh
<interferometry><ligo><detectors><gravitational-waves>
Response function of LIGO
Junaid Ihsan
# Response function of LIGO

(Asked by: username_0 on 2022-01-09)

"Laser Interferometer Gravitational-wave Observatory" (LIGO) is a marvel of precise engineering and the world's largest gravitational wave observatory. LIGO, which consists of two massive laser interferometers separated by 3000 kilometers, uses the physical characteristics of light and space to detect and explain the sources of gravitational waves (GW). <https://www.ligo.caltech.edu/page/what-is-ligo>

**1. What is mean by response or transfer function and what is LIGO  detector's response function?** *(Mathematical Explanation will be preferred)*

**Tags:** interferometry, ligo, detectors, gravitational-waves

> **Comments:**
> **username_1**: A search for "LIGO  detector response function" gives a plethora of scientific papers which deal with the calibration of the LIGO detectors. What exactly are you looking for at what level?  Also you seem to quote a text without giving source of it. Please link the source you quote.  
> **username_0**: @username_1 I added the source, I'm looking for some mathematical concept behind this response function? What mathematical functions are used ?  
> **username_1**: Do you know what a response or transfer function is in physics for a detector? Or are you asking about the details for this particular instrument? Your question is quite unclear on this... What is your prior knowledge on this matter? Please elaborate :)  
> **username_0**: @username_1 kindly see my edited question.  
> **username_2**: @JunaidIhsan in order to write an answer that is helpful, it helps to explain how much you are or are not familiar with the concept of a [transfer function](https://en.wikipedia.org/wiki/Transfer_function) in general. It could take a full chapter of a book to cover everything that *might* cover LIGO's transfer function alone, and that's too much, and after writing a long answer, you might comment "No, that's not what I want to know" or "I know that already" so folks may just not post anything. There are whole books and semester courses on transfer functions!  

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## 1 answers

### Answer by username_1 on 2022-01-09. Score: 3 | Accepted answer

This is a brief and very general answer which points to some papers which deal with LIGO calibration in detail. More detailed answers might be possibly given on either point, but can easily cover complete books each easily, too.

A response or [transfer function](https://en.wikipedia.org/wiki/Transfer_function) of a piece of equipment describes how the device responds to an input signal. This could be in terms of frequency, of photon efficiency, of spatial resolution / diffraction for an optical piece of equipment etc.

Mathematically the detected signal is the convolution of the original (unchanged) signal with the transfer function of the instrument. In order to obtain the original signal you have to know your transfer function and [deconvolve](https://en.wikipedia.org/wiki/Deconvolution) the detected signal with the (hopefully measured and thus well-known) transfer function of your instrument.

In the case of these detectors the most interesting behaviour is the wavelength (or frequency) dependency of the sensitivity of the detectors, thus how well or easily we can detect a signal with a given frequency - possibly as a function of the direction of the signal direction with respect to the sensor orientation.

On the detailed calibration, thus establishment of this particular instrument's transfer function is topic of various works which took years to measure and establish. Some relevant papers on this topic might be these which discuss the sensor calibration prior to measurements - establishment of the sensor's transfer function is essential part of this:

* <https://pure.mpg.de/rest/items/item_795570/component/file_1152583/content>
* <https://dcc.ligo.org/public/0122/P1500248/015/P1500248_EarlyaLIGOCalUncertainty.pdf>

> **Comments:**
> **username_0**: Thanks for answering this question, I was looking exactly the same thing as mentioned in the given papers.  

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