## Coherent Imaging

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. Lets 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
 Recognitions: Science Advisor 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_%28physics%29 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?
 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?

## Coherent Imaging

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
 Recognitions: Science Advisor 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?
 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! Attached Thumbnails
 Recognitions: Science Advisor 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?
 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.

 Tags coherence, coherent, incoherent, optics, telescope