Finding the circle of least confusion for a multi-element optical system

[nevhuan]

Hi,

I'm a mechanical engineer that's new to optics. I'm trying to determine the best location to place an image sensor for an optical system with multiple lenses and mirrors. In doing so, I've come to the understanding that the best position to put the sensor is at the circle of least confusion. However, I have a few questions:

1. Just to confirm, does this mean that the image is no longer formed at the Gaussian focus due to aberrations in the system?

2. From my understanding, the only way to find the circle of confusion is to find the focal point for a ray that enters the entrance pupil of the system at a height of 0.866d or 0.707d etc. I used the information from this website: "[URL ).[/URL] I notice that this only considers spherical aberration. What about astigmatic aberrations etc?

3. Is there a formula I can use in place of paraxial raytracing and aberration calculations?

Many thanks,
N.

 

[nevhuan]

Hi,

I'm a mechanical engineer that's new to optics. I'm trying to determine the best location to place an image sensor for an optical system with multiple lenses and mirrors. In doing so, I've come to the understanding that the best position to put the sensor is at the circle of least confusion. However, I have a few questions:

1. Just to confirm, does this mean that the image is no longer formed at the Gaussian focus due to aberrations in the system?

2. From my understanding, the only way to find the circle of confusion is to find the focal point for a ray that enters the entrance pupil of the system at a height of 0.866d or 0.707d etc. I used the information from this website: "[URL ).[/URL] I notice that this only considers spherical aberration. What about astigmatic aberrations etc?

3. Is there a formula I can use in place of paraxial raytracing and aberration calculations?

Many thanks,
N.

The website is http://www.telescope-optics.net/spherical1.htm"

 

[Andy Resnick]

Hi,

I'm a mechanical engineer that's new to optics. I'm trying to determine the best location to place an image sensor for an optical system with multiple lenses and mirrors. In doing so, I've come to the understanding that the best position to put the sensor is at the circle of least confusion. However, I have a few questions:

1. Just to confirm, does this mean that the image is no longer formed at the Gaussian focus due to aberrations in the system?

Yes- aberrations change the shape and location of the point spread function. Object points do not get mapped to an Airy disk, and the Airy disk is not uniform over the image plane.

2. From my understanding, the only way to find the circle of confusion is to find the focal point for a ray that enters the entrance pupil of the system at a height of 0.866d or 0.707d etc. I used the information from this website: "[URL ).[/URL] I notice that this only considers spherical aberration. What about astigmatic aberrations etc?

It has been a while since I've done detailed ray tracing, but AFAIK the answer to the first question is 'not really'. The ray heights 0.866 and 0.707 correspond to the 'midpoint' (0.707) and 75% (0.866) of the entrance pupil diameter, those were chosen for convenience (and now, convention). But, in order to locate the circle of least confusion, a detailed ray trace must be performed.

Other aberrations will change things as well- astigmatic aberrations result in a 'medial' focal plane, similar to the circle of least confusion. Coma is another common aberration in telescope optics: off-axis stars are imaged as elliptical blobs.

3. Is there a formula I can use in place of paraxial raytracing and aberration calculations?

Many thanks,
N.

I don't know of a simple formula that gives you the results you want. Ray tracing is fairly simple to perform (although it's also time consuming to perform by hand)- you can implement a ray trace algorithm in Excel, and there may even be semi-free programs available.