Optimization problem (imaging science)

In summary, the question is asking for the optimal source-to-object distance and the FWHM of the total PSF at the object plane. Using the equations provided, the optimal source-to-object distance is found to be 96.1cm, and the FWHM of the object PSF is 0.98mm. The 'a' dependent factor in the FWHM object plane equation is needed to solve for 'a' and is found by taking the derivative and setting it equal to 0. No exponentials are necessary in this problem.
  • #1
richard7893
18
0

Homework Statement



Assume a transmission imaging system with the following parameters: focal spot PSF
equal to a Gaussian with FWHM = 0.5 mm, a detector PSF equal to a Gaussian with
FWHM = 0.1 mm, source-to-detector distance = 100 cm. Compute:
1. the optimal source-to-object distance
2. the FWHM (in mm) of the total PSF at the object plane at this optimal source-to object distance.




Homework Equations



a= S1/(S1+S2); b=S2/(S1+S2); where S1 is the distance from focal spot to object, S2 is the distance from the object to the detector, & S1+S2 is the distance from the focal spot to detector (100cm).

a+b=1 (S1 + S2 have to add to 100cm, the detector-source distance)

FWHM_object plane = ( (an 'a' dependent factor *FWHM_focal spot)^2 + (an 'a' dependent factor *FWHM_detector)^2)^(1/2) ==> (pythagorean, in case the text looks confusing. Hard doing this without pencil & paper).


The Attempt at a Solution


I know I have to take the derivative wrt 'a' of the FWHM_obj plane equation, set it equal to 0 and solve for 'a'.

I know at this distance,'a', the PSF of the object is smallest because it's FWHM is at a minimum, making that location the optimum place to put the object.

Ultimately I'm trying to solve for S1 which I'll know once I find the value of 'a'.

The answer is supposed to come out to: 96.1cm, this is how far the object needs to be from the focal spot. And the FWHM of the object PSF is 0.98mm. I just don't know how to arrive at these numbers.

My teacher gave me the above equations, but I just don't know what the 'a' dependent factor needs to be.

And my prof. also said I didn't need to use any exponentials, even though the problem mentions gaussian functions in it.

Any help will be appreciated.
 
Physics news on Phys.org
  • #2
any answers ?
 

1. What is an optimization problem in imaging science?

An optimization problem in imaging science involves finding the best possible solution for a specific imaging task, such as image reconstruction, denoising, or segmentation. This involves finding the optimal values for a set of parameters or variables that will result in the most accurate or desirable image.

2. What are some common optimization techniques used in imaging science?

Some common optimization techniques used in imaging science include gradient descent, simulated annealing, genetic algorithms, and particle swarm optimization. These methods involve iteratively adjusting the parameters of an imaging algorithm to minimize an objective function, such as mean squared error or cross-entropy loss.

3. How do optimization problems in imaging science differ from other optimization problems?

Optimization problems in imaging science often involve unique challenges, such as dealing with noisy or incomplete data, or incorporating constraints based on physical or biological principles. Additionally, the objective function used in imaging science may differ from those used in other optimization problems, as it may be based on perceptual quality rather than mathematical accuracy.

4. What are some applications of optimization problems in imaging science?

Optimization problems in imaging science have a wide range of applications, including medical imaging, remote sensing, computer vision, and digital photography. They are used to improve image quality, enhance image features, and extract useful information from images in various fields.

5. What are some challenges in solving optimization problems in imaging science?

Solving optimization problems in imaging science can be challenging due to the high dimensionality of the parameter space, the non-convex nature of the objective function, and the potential for overfitting or underfitting. It may also require a significant amount of computational resources and expertise in both imaging science and optimization techniques.

Similar threads

I Using simple lenses to image AFM Probes
    • Optics
Replies
10
Views
1K
Image distance of a Keplerian telescope
    • Introductory Physics Homework Help
Replies
7
Views
1K
Building a small pattern projector
    • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
Hexapod Leg Design: Optimizing a 3D Printed Femur Assembly
    • Mechanical Engineering
Replies
1
Views
1K
A Thought experiments suggest problem with published work
    • Optics
Replies
8
Views
1K
Numerical aperture of a Keplerian telescope
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
Would this have been optimized by a compiler?
    • Programming and Computer Science
Replies
3
Views
928
A Mode matching to an optical cavity
    • Atomic and Condensed Matter
Replies
0
Views
293
I Lateral offset from a centered star as measured at the focal plane
    • Astronomy and Astrophysics
Replies
3
Views
867
I Time of flight measurement uncertainty
    • Classical Physics
Replies
3
Views
935

Hot Threads

Recent Insights

Back
Top