Since a collimated beam is always in focus, can't I simply just emit a collimated beam over the varying distances as the target object moves?

Question

I am designing an interferometer for an experiment. The setup consists of (1) the laser source, (2) the interferometer itself (consisting of optical components and photodetector(s)), and (3) the target object. Once the laser source emits into the interferometer setup, it first encounters a spatial filter. This spatial filter converts the low-quality, rapidly diverging beam of the laser diode into a high-quality, collimated beam. Once the beam exits the spatial filter, it enters a beam splitter. This beam splitter allows part of the beam to be emitted at the target, and part of the beam to go deeper into the interferometer setup. The interferometer then depends on light reflected back into the interferometer from the target object.

1. Light being emitted at the target object:

2. Light being reflected from the target object back into the interferometer:

I have seen interferometer setups that have an aspheric lens at the aperture of the interferometer system. The aspheric lens seems to be orientated so that the light leaving (being emitted from) the interferometer is focused, and the light entering (reflected back into) the interferometer is collimated. This is illustrated in these diagrams:

(From https://en.wikipedia.org/wiki/Interferometry#Biology_and_medicine )

(From https://pubs.rsc.org/en/content/articlelanding/2019/ay/c9ay00369j/unauth )

1. Light being emitted at the target object (now including an aspheric lens):

2. Light being reflected from the target object back into the interferometer (now including an aspheric lens):

However, the problem is that my target object distance, from the aperture of the interferometer to the target object, varies between 10-100cm. This means that, if the optics at the aperture of the interferometer give the emitted beam a fixed focus, as an aspheric lens would, the beam would be out of focus when incident upon the target object. And, so, this would decrease the performance of my interferometer. Therefore, I don't want optics at the aperture of the interferometer that result in a fixed focus (such as an aspheric lens), since that wouldn't properly focus the beam for a varying-distance target.

But I had an idea to get around this. Since I'm using a spatial filter with aspheric lenses (see slides 13/14 here) immediately after the laser source in order to collimate the beam and get it to a high quality state, and since a collimated beam is, as I understand it, always in focus, can't I simply just emit the collimated beam over the varying distances as the target object moves (as shown in the first two diagrams), rather than having the fixed-focus optics (the aspheric lens) at the aperture of the interferometer (as shown in the last two diagrams)? It seems to me that, as long as the beam is relatively well-collimated (which it should be from the spatial filter), and as long as the distance isn't too far (which, for 10-100cm, it shouldn't be), this would mean that the beam will be in relatively good focus when incident upon the target object.

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Answer 1

If I understand your question, you could just use a collimated beam exiting from the interferometer. However, you don't clearly state what is the "aperture" of the interferometer. I assume you mean the arm that leaves the beamsplitter cube at 3 oclock, this is commonly called the "test arm". But, if you use a collimated beam, there are a lot of issues that may prevent the interferometer from doing what you want it to do. If the target region where the test arm beam hits has multiple regions that differ in height by several wavelengths, then the signal back to the interferometer will consist of not just one, but several wavefronts. These multiple wavefronts may (i.e. likely will) constructively or destructively interfere. This means you'll get a mixed result for the interference signal. You will sacrifice spatial resolution in the direction perpinducular to the probe beam.

If the target region where the test arm beam hits has multiple regions that differ in angle, the return beams will be angularly dispersed going back to the interferometer. They may not make it through the interferometer or they may not hit the detector.

If your source has very low temporal coherence, you'll have to move the reference arm in z in order maintain interference between the test and reference arms. This is what most OCT setups do. In general, any interferometric measurement device (whether OCT or not) is a compromise between resolution and range. I would recommend looking in the literature to find how people configured systems that measured the range you want.