## Detection of Exoplanets

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oopfan
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### Detection of Exoplanets

Hi Robin,

I wanted to run some math by you. I am trying to determine if my Altair 290M has what it takes to measure the light curve of Qatar 1b.

According to published works the depth of minimum light is +0.03m. I've attached my sensor analysis for MONO12 for your reference.

Step 1 is to find the number of Stops associated with a difference of 0.03m. That turns out to be 0.03986. (Thank you Wikipedia and my undergraduate Astronomy professor.)

The next several steps should be repeated for each Gain Value in the sensor analysis table:

Step 2 is to divide 0.03986 by "Dynamic Range (Stops)" for a given Gain Value. Let's take the first row for Gain 100, hence, 0.03986 divided by 12 is 0.3322%.

Step 3 is to multiply 0.3322% by the number of levels of a 12-bit ADC, hence 0.3322% multiplied by 4096 is 13.607 ADU.

Step 4 is to multiply 13.607 ADU by the number of electrons per ADU, hence 13.607 times 1.82 e/ADU is 24.764 e.

Step 5 is to compute the signal-to-noise ratio by taking the square root of 24.764 divided by the Read Noise of 1.59e which is 3.95 SNR.

Then we repeat Step 2 through 5 for each Gain Value we get the results in the final attachment.

From what I understand the signal is indistinguishable from noise for a Gain Value of 3600.

My gut tells me to choose gains having a SNR of 2 or greater (i.e. Gain Values of 100-600 are good.)

Thank you for your input Robin.

Brian
Attachments
Altair GP290M Sensor Analysis MONO12 Cropped.png (104.31 KiB) Viewed 261 times
SNR of 0.03m difference MONO12.png (3.42 KiB) Viewed 261 times

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### Re: Detection of Exoplanets

Hi Brian,

I think I'd come at the problem from a different angle as follows

* Delta magnitude is 0.03, turn that into a fractional changing in brightness with the standard magnitude formula ( 10^(-0.4m) ) - by my calculation that gives a brightness of 97.3% of normal during the occultation phase, or a reduction of 2.7%

* Full well at minimum gain is ~7500 electrons. You would want to nearly (but not quite) saturate the star to get the best measurements - let's say 7000 electrons per exposure

* Shot noise for 7000 electron exposure is sqrt(7000) = ~84 electrons. This is much bigger than the read noise, so we can ignore the read noise completely

* The noise level is about 1.2% of the total 7000 electrons, so this is looking promising

So the signal you are trying to detect is a change of about 2.7% and the noise level in a single 7000e exposure is 1.2%, so I think you have a good chance if you can take multiple exposures at 7000e each during the occultation time ( a single exposure would likely show the signal, but it is only about 2x noise level, so you wouldn't be able to claim a statistically significant result on one exposure).

Note that the 290 sensor has the ability to switch begween HCG and LCG modes (High conversion gain, low conversion gain). Your results look to be in the HCG mode which gives lower read noise but also lower full well depth. It should be possible to get a FWD of about 15000 at minimum gain in LCG mode, which will reduce your shot noise % by a factor of Sqrt(2).

I think your original analysis falls down because you have not included the effects of shot noise.

cheers,

Robin

PS - I really hope that you get this to work!

oopfan
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### Re: Detection of Exoplanets

Thank you, Robin! This will be very, very interesting. I will start with HCG since I think I need the shortest possible exposure. My mount is far from optimal. I only have a motor drive in RA. There is no active guiding. I rely on precise polar alignment and my do-it-yourself PEC solution. In the past I've gotten acceptable results with 2 minute exposures for DSO's but Photometry is a totally different beast. Ideally I want to keep the Airy disk precisely on top of the same pixel(s) for the duration of the exposure. I may have to experiment with defocusing the star and/or choose only brighter stars to measure. Last night I visited the AAVSO website. They have a good database of variable stars. I think I will start there before graduating to Exoplanets.

oopfan
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### Re: Detection of Exoplanets

Hi Robin,

In the second to last paragraph you wrote:

"( a single exposure would likely show the signal, but it is only about 2x noise level, so you wouldn't be able to claim a statistically significant result on one exposure)"

I reread your tutorial on "Picking the correct exposure for Deep Sky" but I am at loss to answer this question:

If stacking were not an option what multiple of the noise level would be considered statistically significant in a single exposure?

Thanks,
Brian

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### Re: Detection of Exoplanets

Hi Brian,

if your signal is 2x the noise level then you are two standard deviations (2σ) away from the mean. This means that there is a chance of getting the same result just because of random fluctuations and for being 2σ lower than the mean the chance is about 2.5%, meaning that if you took 40 measurements of the star then roughly one of them would look like it was obscured even if it wasn't just due to random variations in the brightness of the star.

For particle physics discoveries they aim for a target of 5σ (5 standard deviations away from the mean) before they announce a result - the chance of that happening at random is about 1 in 4 million. (See the table here for the figures - https://en.wikipedia.org/wiki/Standard_ ... buted_data - remember that the probabilities they give are for being at least that far away in either direction, so halve the probability if you are only interested in one direction).

Suppose you wanted to aim for an SNR of 4σ, which has a chance of 1 in about 30000 of happening at random. To get that confidence you'd need to double your SNR (so either double the signal or halve the noise). The only way to increase your SNR is to collect more photons, since the SNR is basically equal to the square root of the number of electrons (and therefore proportional to the square root of the photons collected).

Collecting more photons options:

1) Longer exposures - but you must not saturate, so limited there
2) Stacking
3) Defocus the star so that you collect the light over many pixels, then longer exposures until those pixels are nearly saturated, then measure the total electron count across all pixels in the star.

cheers.

Robin

oopfan
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### Re: Detection of Exoplanets

Thank you, Robin.

I joined the AAVSO the other day and yesterday I enrolled in a 4-week course on CCD Photometry (Part I). I am hoping that all of this will come into clearer focus (excuse the pun.)

Brian

oopfan
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### Re: Detection of Exoplanets

Hi Robin,

Now I see the benefits of LCG.

Question: LCG/HCG is not switchable from SC's control panel but it is from AltairCapture. Having said that I don't think that SC will allow me to keep two sets of Sensor Analysis results if it is not reading the LCG/HCG setting on the camera. But this could work more easily if there was a SC option to select a prefix for the sensor analysis files. So for example if I know that the camera is in LCG mode then I would go to SC settings and specify LCG (i.e. type it in) before opening the camera for use. Without this capability I will need to go to the file system and rename the files.

Thanks,
Brian

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### Re: Detection of Exoplanets

Hi,

SharpCap applies an automatic switch between LGC (gain 100-199) and HGC (gain 200+), for the simple reason that this approach provides the best quality images throughout the gain range without the user needing to worry about it. You should always use HGC if it's an option because it provides a lower read noise than LGC when both are set up for the same e/ADU gain and full well depth. However, the low gain, high full well, range cannot be reached in HGC mode, so SharpCap selects LGC automatically.

SharpCap also understands the switch between LGC and HGC mode happening at gain 200 without needing to have two sets of sensor data saved - have a look at the sensor analysis graph (which you can do now in the Brain window) and you'll see the step change in read noise at 200 gain, but a smooth e/ADU curve.

cheers,

Robin
Capture.PNG (12.74 KiB) Viewed 192 times

oopfan
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### Re: Detection of Exoplanets

All right now, the secret was to rerun Sensor Analysis. Apparently the software changed in a significant way since I originally ran it on November 26, 2017.

Would you recommend rerunning Sensor Analysis for each new beta release until 3.1 is officially released?
Attachments
Altair GP290M Sensor Analysis MONO12 2018-01-09.png (89.14 KiB) Viewed 179 times

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### Re: Detection of Exoplanets

Hi,

the answer to your question is basically yes - I'd hoped that 3.1 was nearly finished, but I've discovered that ZWO some sensors don't behave in the way I was expecting, so I need to re-write some of the code then those sensors will need to be re-measured...

I try to make changes to this backward compatible, but it doesn't always work out.

cheers,

Robin

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