Question Regarding Guiding Accuracy

[Chris Willocks]

Hi everyone,

I'm wondering if someone can kindly explain to me in very simple terms how the following factors affect guiding accuracy in relation to each other:

• Mount accuracy i.e. PE RMS.
• Imaging camera pixel scale.
• Guide camera pixel scale.
• Seeing.

From what I've read, the ideal mount PE RMS (unguided or guided) should be half the pixel scale of the imaging camera? Is this correct, or is it half of the guide camera?

How are the imaging camera and guide camera pixel scales related when it comes to guiding accuracy? Is there an optimum ratio between the two?

How does seeing come into all this?

I'm just trying to understand how to assemble the optimum setup, in terms of obtaining the best guiding accuracy. For example, if we had the below equipment setup, would this give ideal guiding accuracy for imaging small objects, such as galaxies:

• Scope: Esprit 150ED.
• Mount: CEM120EC2 (PE < 0.15" RMS).
• Imaging camera: SX Trius SX-814 (Image scale: 0.72" per pixel).
• Guide camera: Lodestar X2 with SX OAG (Image scale: 1.61" x 1.65" per pixel).

Hopefully this makes sense.

Many thanks,

Chris

[cuivenion]

 

[vlaiv]

Here are some pointers and explanations:

Mount PE RMS and P2P are somewhat important - What is more important is smooth and slow changing PE. This enables you to guide your mount to greater accuracy. When analyzing PE data you need to pay attention to maximum rate of PE change - that is expressed in "/s. This value is used to determine max deviation from position in one guide exposure. Let's say max rate of change is 0.1"/s. In 4s exposure at that speed mount will move off target 0.1"/s * 4s = 0.4".

Average of these deviations is what is guide RMS error. Larger deviations and more often - larger RMS error of guiding. Hence you want to minimize that.

Going with shorter exposures makes it difficult to tell if star position changed due to seeing or was it due to mount.

With mount you mentioned you don't have to think of PE error of the mount. That mount has encoders and it does RPEC - or real time periodic correction. It samples encoders and direct mount to track at proper rate. You will still benefit from guiding, as PE is not the only thing affecting star position.

When choosing guide setup, important thing to remember is that you need good resolution to measure star position with enough precision. I would strongly recommend OAG and camera with smaller pixels. With such large scope and resolution you are intending to use (which I believe is too much, but that is another topic) you need your guiding to be the best possible. That would mean less than 0.3" RMS (about 0.1 - 0.15" RMS would be ideal). This means that you need at least 3 times lower centroid precision, but 5-6 times lower would be better - meaning 0.05" centroid precision. Centroid precision is about 1/16 to 1/20 of pixel size - when we account for that, you need guiding resolution of about 1"/px.

I like your setup, but I would look into maybe changing 2 things. Get CMOS guider camera with smaller pixels. If they are too small you can bin them to get a bit better star SNR. I do it on my setup, bin cmos pixels and that way get to 1"/px resolution.

Maybe revise your intended imaging resolution. If you want CCD - look at one giving you about 1"/px. If going for CMOS, you can choose one giving you 0.5-0.6" and bin afterwards, or go with one giving you 1-1.1" natively.

[Chris Willocks]

1 hour ago, vlaiv said:

This means that you need at least 3 times lower centroid precision, but 5-6 times lower would be better - meaning 0.05" centroid precision. Centroid precision is about 1/16 to 1/20 of pixel size - when we account for that, you need guiding resolution of about 1"/px.

Thanks for explaining.

Am correct in saying that the RMS of less than 0.3" is based on the half the value of the image scale of the imaging camera i.e. 0.72"/px?

Also, just out of curiosity, how did you calculate the guiding resolution of 1"/px stated above?

Wouldn't the centroid precision be limited by seeing? For example, if you had a seeing of 2", that would mean that the optimum sampling based on the Nyquist Theorem would be 0.67"/pixel.

So if you work backwards (assuming that centroid precision is 1/16 x pixel size):

0.67"/ pixel x 16 = 10.72"/pixel.

So, in other words, anything below 10.72"/pixel resolution for the guider wouldn't make any difference in this case, due to being limited by seeing?

Have I got this correct?

Thanks,

Chris

[vlaiv]

1 hour ago, Chris Willocks said:

Thanks for explaining.

Just out of curiosity, how did you calculate the centroid precision of 0.05" and guiding resolution of 1"/px stated above? Is there a formula to calculate these?

Also, am correct in saying that the RMS of less than 0.3" is based on the half the value of the image scale of the imaging camera i.e. 0.72"/px?

Thanks,

Chris

Centroid precision is often quoted to be between 1/16th of a pixel and 1/20th of a pixel. If guiding resolution is 1"/px - this means that pixel side covers 1" and precision of 1/20 of that is 1" / 20 = 0.05".

If we apply quoted figures to the letter, then actual star centroid precision would be between 1"/20 and 1"/16 or in range of 0.05" to 0.0625".

On the matter of needed guide precision, yes, there is general rule of thumb that says RMS should be half the imaging resolution or less. It's a good rule, but I did not go by that. There is more involved but also more precise estimation of performance of system. It is based on estimation of star FWHM in images based on aperture size, seeing conditions and guiding RMS error.

This for example, under very good conditions like 1" FWHM seeing and 0.3" RMS guide precision for 150mm scope gives expected star of about 1.5" FWHM and that corresponds to 0.94"/px. For slightly different parameters like seeing of 1.5" FWHM same scope and same guiding will give FWHM of 1.87, or optimum sampling rate of 1.17"/px

This shows that optimum resolution is not always related to guide precision in 1:2 ratio, but under most circumstances - meaning most amateur apertures 3"-8" and under most seeing conditions it is close enough.

I mentioned very good guiding, because a) I expect your listed mount to be able to provide it without breaking a sweat, and b) because you went for high sampling rate at 0.72"/px and for that imaging resolution not to over sample with 6" scope good guiding and good seeing will be needed - I mean very good. Look at the above calcs - both optimum sampling rates are around 1" and 0.72" is 30% less of that.