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Loconel
2014-May-16, 02:01 PM
Can someone tell met why the JWST has a focal length of 131.4 meter.
I assume it is calculated from the focal length of each mirror and the distance between the mirrors.
Please show me the calculation

Can the answer be found in this document? http://www.handprint.com/ASTRO/ae2.html

regards, Louis
the Netherlands

Hornblower
2014-May-16, 03:59 PM
Can someone tell met why the JWST has a focal length of 131.4 meter.
I assume it is calculated from the focal length of each mirror and the distance between the mirrors.
Please show me the calculation

Can the answer be found in this document? http://www.handprint.com/ASTRO/ae2.html

regards, Louis
the Netherlands

Are you asking why that focal length was chosen by the designers, or are you asking how to calculate it from the focal lengths of the mirrors and their spacings?

StupendousMan
2014-May-16, 04:58 PM
One facet of the design is the size of the pixels in the detectors. One of the detectors, NIRSpec, has pixels which are d = 18 microns on a side. If this detector is placed behind a telescope with effective focal length of f = 131.4 meters, then the angular size of each pixel is

angular size = atan( d / f ) = 7.85 x 10^(-6) degrees = 0.028 arcsec

This is very roughly the same as the diffraction limit of the telescope at a wavelength of 1 micron:

diffr limit = approx ( lambda / D ) = ( 10^(-6) m / 6.5 m ) = 1.5 x 10^(-7) rad = 0.032 arcsec

In most circumstances, one should roughly match the angular size of one's detector pixels to the diffraction limit: that way, you are getting the maximum out of your telescope and detector at the same time.

Amber Robot
2014-May-16, 06:00 PM
In most circumstances, one should roughly match the angular size of one's detector pixels to the diffraction limit: that way, you are getting the maximum out of your telescope and detector at the same time.

This.

glappkaeft
2014-May-16, 06:08 PM
LWST is a three mirror anastigmat design with an slighly offset light path using an extra flat mirror (for fine steering) and most optics texts don't cover those. There is an image with all the important design statistics at http://opticalengineering.spiedigitallibrary.org/data/Journals/OPTICE/22177/OE_51_1_011003_f008.png that could be used to to do the calculations if you can figure out how.

The research papper D. Korsch, "Closed Form Solution for Three-Mirror Telescopes, Corrected for Spherical Aberration, Coma, Astigmatism, and Field Curvature," Appl. Opt. 11, 2986-2987 (1972), might help but it is behind a pay wall.

glappkaeft
2014-May-16, 06:15 PM
In most circumstances, one should roughly match the angular size of one's detector pixels to the diffraction limit: that way, you are getting the maximum out of your telescope and detector at the same time.

I have two minor quibbles with this. The first is that you should only match the diffraction limit if you are designing a space telescope, earth bound telescopes are always seeing limited unless they are smallish amateur instruments. The second is that it is actually better to do it the other way around, suitable CCD cameras come in a small range of pixel sizes while telescopes can easily be designed with almost any focal length or aperture.

StupendousMan
2014-May-16, 08:44 PM
I have two minor quibbles with this. The first is that you should only match the diffraction limit if you are designing a space telescope, earth bound telescopes are always seeing limited unless they are smallish amateur instruments. The second is that it is actually better to do it the other way around, suitable CCD cameras come in a small range of pixel sizes while telescopes can easily be designed with almost any focal length or aperture.

I have been successfully quibbled.

Let me send back a quibble of my own: when one is talking in particular about an infrared-optimized space telescope, I'm not sure that there are, in fact, a large range of solid-state detectors (CCDs don't work in the infrared) with different pixel sizes from which one can choose.

Amber Robot
2014-May-16, 08:52 PM
I have two minor quibbles with this. The first is that you should only match the diffraction limit if you are designing a space telescope, earth bound telescopes are always seeing limited unless they are smallish amateur instruments. The second is that it is actually better to do it the other way around, suitable CCD cameras come in a small range of pixel sizes while telescopes can easily be designed with almost any focal length or aperture.

Earth-bound telescopes can be diffraction limited using adaptive optics. Or at the very least, they can go below the seeing limit. It also depends on wavelength.

As a general rule, a good design should take into account the relationship between the image angular resolution and the detector resolution in such a way as to maximize sensitivity to astronomical sources.

Shaula
2014-May-16, 08:53 PM
CCDs don't work in the infrared
Many of the common ones have a quantum efficiency of above 20% out to 900nm, which is near infrared. That was one of the reasons they had to put NIR blockers into camcorders - the CCDs in them were picking up lots of NIR and back in 1998 Sony had a publicity nightmare when a model of camcorder they sold had a nasty habit of 'seeing through' thin clothing.

I quibble with the counter-quibble to the quibble.

Swift
2014-May-16, 09:08 PM
I quibble with the counter-quibble to the quibble.
One more and we'll have a quad quibble. :D

StupendousMan
2014-May-16, 10:12 PM
When I wrote "space telescope optimized for the infrared" -- as JWST is -- I meant "optimized for wavelengths as long as 5 microns", which would knock CCDs out of the running.

I've lost track of the number of quibbles :-/

Shaula
2014-May-17, 04:07 AM
That's the Quouble with Quibbles.

glappkaeft
2014-May-17, 02:55 PM
Its Quibbles all the way down...

On a more serious note I'm no longer certain the image I posted contains enough information to make a completly accurate model of JWST. Since the light path is tilted the teriary mirror is made out of just a part of a larger mirror and I can't find this information nor the information on the tilt itself. Someone who knows optics could probably calculate this but I'm just a dabbler when it comes to optics.

Loconel
2014-May-17, 10:12 PM
Thank you. With this information I can ask someone with knowledge of a Cassegrain telescope if he can figure out why