Understanding Coherent Imaging in Optics: An Example

In summary, in optics, there is coherence and incoherence. The degree of coherence is determined by the size of the Point Spread Function (PSF). To determine if an image is coherent or incoherent, you need to know the spectral and spatial extent of the source, as well as the imaging properties of your system.
  • #1
eschiesser
18
0
This is a very vague question, but I hope by asking it, we can pin down an answer eventually.

In optics, there are such things as "Coherent Imaging" and "Incoherent Imaging." From what I understand, the degree of coherence has to do with the size of your Point Spread Function (PSF), a.k.a. the image of a point source a.k.a. d=1.22*wavelength/NA and the correlation of phase over many times the PSF at your image plane.

Given that understanding, what exactly would I need to know about an optical system and whatever it is imaging to determine the degree of coherence?

Lets set up an example:

We're imaging a black-white grating on the moon (avg distance 400,000 km) with a period of 1km. Let's assume that the sun is illuminating the grating, and my eye has a pupil diameter of 7mm and can resolve 2 point sources separated by 1 minute of arc, and I am imaging with a telescope. Is this coherent or incoherent? Do I need any other information to tell?

The way I've set it up, this would seem incoherent. But on what grounds? How can I tell? What determines coherence!?

Anything and everything appreciated.

-Eric
 
Physics news on Phys.org
  • #2
There seems to be a lot of confusion here. Coherent imaging refers to the ability to detect the field, rather than the intensity. That is, in addition to the amplitude, the phase is also recorded. An intensity detector can be used in coherent imaging, but there must be a way to image the phase information- for example, interference fringes.

The coherence properties of the source can impact the imaging properties of a system- Goodman's "Fourier Optics" has an excellent chapter about this. The coherence properties of the source are really given by the spectral and spatial extent of the source, not by the PSF (except in specific circumstances).

http://en.wikipedia.org/wiki/Coherence_(physics)

Note, the PSF for an incoherent system is different than the PSF for a coherent system- again, Goodman's book covers this amazingly well.

As per your example, the sun is a fairly spectrally incoherent source, and unless the grating has some phase information, since your eye can only respond to intensity, this is incoherent imaging. If you made the grating a phase-only object, unless you had an optical system that converted the phase information into intensity information (see, for example, phase contrast imaging), you would still have incoherent imaging.

Does this help?
 
  • #3
Yes Andy, I suppose it does. It is essentially a confirmation of my intuition, but I am still uncertain about what my professors mean when they ask me about the coherence of a system. Perhaps this is a question for them.

So, what role does my imaging system play in the coherence of my image, in the context of pupil shape/diameter, or is it entirely determined by my illumination source?
 
  • #4
Here's a quote from my notes:

"For a given 'Illumination Aperture Stop', the degree of coherence depends on the size of the Pupil Plane Aperture (i.e. resolution)."

and

COHERENT ILLUMINATION (in context of a microscope with Koehler Illumination)
Remember the size of the Pupil determines the size of the coherent impulse response. Big pupil transmission function implies narrow impulse response. And a small illumination aperture stop image implies wide coherence. The coherence of the illumination across the object is broader than the impulse response. Neighboring spots on the object have a fixed phase relationship. Image is composed of a collection of amplitude impulse response, which add in amplitude i.e. Coherent -> Amplitude

that's all from the notes from Professor Jim Zavislan
 
  • #5
Ok.

Consider the role of the aperture stop (entrance pupil). On the illumination side, the aperture stop acts to change the apparent size of the source, and this changes the spatial coherence at the sample. It's the same as using a color filter to change the spectral coherence of the illumination.

Koehler and critical illumination are very similar- one is the Fourier transform of the other. For Koehler illumination, increasing the aperture stop is equivalent to decreasing the apparent source size *as seen by the sample*, and thus the spatial coherence of the illumination increases. Alternatively, since the numerical aperture of the illumination increases, the size of the illumination PSF decreases.

On the detection side, the aperture stop (exit pupil) controls the cutoff spatial frequency. The total resolution of the optical system is given by both the illumination numerical aperture and the detector numerical aperture, and this is the motivation for slightly stopping down the illumination aperture when the objective has a lower NA than the condenser- the high spatial frequencies are attenuated, but the contrast at mid-range spatial frequencies (which are associated with "good images") is increased.

"The coherence" of a system is difficult to calculate, except in limiting cases. Examples of coherent imaging methods in microscopy include phase contrast and differential interference contrast, because interference is used to convert phase-only information to intensity information at the detector. Changing the aperture stop while performing DIC imaging may be instructive.

Confocal methods use highly coherent sources (single frequency, small size), but because of the detector are incoherent imaging systems.

Pure coherent detection is currently possible only below GHz frequencies (AFAIK- I've seen some noise about coherent THz detectors), and use technologies like homodyne/heterodyne detection.

How's that?
 
  • #6
Excellent, Andy.
I saw these posts while searching answers and solutions for my custom-built miscroscope. The microscope I built is 20X, and I am using it to inspect some micro-structure samples. I tried two different illumination system. The first illumination system focuses a single wavelength LED to the sample (a micrometer) to illuminate it, the image quality seems great, see attached "LED Illumination.jpg". The second system focuses the single wavelength beam coupled into the system with a fiber to illuminate the micrometer, the image degraded. In the attached "Fiber Optic Illumination.jpg", you can see the bright borders around the black division marks. Here are my questions:

1. Is this degradation caused by defraction? I understand that the fiber increases the spatial coherence of the illumination beam. Could the NA of the focusing lens contribute to this? By the way, the division of the micrometer is 10um

2. Is there a solution to improve the image quality when a fiber optic cable is used to illuminate the sample?

Thanks!
 

Attachments

  • LED Illumination.jpg
    LED Illumination.jpg
    38.2 KB · Views: 667
  • Fiber Optic Illumination.jpg
    Fiber Optic Illumination.jpg
    42.5 KB · Views: 708
  • #7
I don't understand how you are illuminating the sample- in the first case, is the LED shining directly onto the sample, or is there a condenser lens? In the second, I have the same question and additionally, what kind of fiber is it- single-mode, multi-mode, fiber bundle, etc.. Lastly, some of the image features could be due to defocus/spherical aberration- how much control do you have over the focus movement (i.e. z-axis resolution), and how well can you locate the plane of best focus?
 
  • #8
1. In the LED illumination, both collector and condenser lenses are used. These are moded glass asphric lenses with 25 focal length. The condenser is very close to the sample.

2. In the fiber illumination, a multi-mode fiber is used. A single precision-polished asphric lens is used to focus the beam on the sample. The distance between the focusing lens and the sample is much larger than the first case.

3. A micro-stage is uded to focus the objective lens to the sample. The focusing lens position is adjusted by hand and thus has less control, but from my experience working on these two different illumination system, it is unlikely the cause.
 

1. What is coherent imaging in optics?

Coherent imaging in optics is a technique used to produce high-quality images by using a coherent light source, such as a laser, to illuminate an object. The light waves reflected or transmitted by the object are then combined to create an interference pattern, which is captured by a detector and converted into an image.

2. Why is coherent imaging important in optics?

Coherent imaging allows for the production of high-resolution images with excellent contrast and detail. It is particularly useful in microscopy, holography, and other applications where precise imaging is crucial. Additionally, coherent imaging can be used to study the properties of materials and biological samples at a nanoscale level.

3. What is an example of coherent imaging in optics?

One example of coherent imaging in optics is optical coherence tomography (OCT). This technique uses a low-coherence light source to create high-resolution cross-sectional images of biological tissues, making it a valuable tool in medical diagnostics and research.

4. How does coherent imaging differ from incoherent imaging?

Coherent imaging uses a single coherent light source, while incoherent imaging uses multiple incoherent light sources. This results in a loss of coherence and reduced image quality in incoherent imaging. Additionally, coherent imaging can capture phase information, which is not possible with incoherent imaging.

5. What are the challenges in achieving coherent imaging in optics?

One of the main challenges in coherent imaging is maintaining the coherence of the light source. Any vibrations, temperature changes, or imperfections in the optical setup can disrupt the coherence and result in degraded image quality. Another challenge is dealing with noise, which can also affect the coherence and lead to artifacts in the image.

Similar threads

Replies
13
Views
1K
  • Electromagnetism
Replies
20
Views
1K
Replies
14
Views
1K
  • Astronomy and Astrophysics
7
Replies
226
Views
10K
Replies
4
Views
1K
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
808
Back
Top