Microscopes and imaging

We’ve acquired enough images of computer chips to start performing a systems analysis of the microscope and determine what needs to be improved. Here’s what we have been using to acquire images:

Zeiss Ultraphot. This microscope has two light paths- as a compound microscope and as a simple microscope. As an aside, while it is true that compound microscopes are by far more common than the simple microscopes in a laboratory setting,the phrase “Though now considered primitive…” is unfairly dismissive, as evidenced by the posted images (IMHO).

In any case, until very recently we have been using the ultraphot in the compound microscope configuration. An industry standard is to connect digital cameras to microscopes via a c-mount (similarly, telescopes generally use a T-mount or here). The problem has been that the sensor size (35mm format) is large enough so that the optical limitations become apparent- the image underfills the sensor, and image quality degrades rapidly away from a well-corrected center region. It turns out that these problems are related to each other, and are also a consequence of the optical characteristics of the human eye.

Compound microscopes have an additional piece, as compared to simple microscopes. This piece, the eyepiece, is used to project the image from the objective lens onto your retina. Optical designs of eyepieces are highly complex for a variety of reasons, and in addition, it must satisfy constraints created by the human eye. In technical terms, the eyepiece needs to have an exit pupil that is the same size as the diameter of the eye pupil, about 5mm, and the image size should be matched to the size of your retina, about 20mm in diameter. But what does have to do with an image formed at the camera? It would seem that we wouldn’t need an eyepiece for the camera- there’s no lens on the camera like there is in our eye….

It matters because the primary image does not have to be very large (even a 2mm image size is sufficient for a 10x eyepiece), and the field of view of the objective does not have to be very large either due to the small pupil size. The entire microscope body is constructed based on the fact that most optical components don’t have to be much larger than 20mm in diameter.

The lightpath from the objective lens to the CCD is really simple- empty space (the ‘tube length’). So the ‘primitive’ simple microscope is an essential component of all research-grade microscopes… Now, here’s a neat tick- since there’s no lens in between the objective lens and the CCD, if I vary the distance between the CCD and the objective lens, I can vary the magnification (by refocusing as I move the CCD). To be sure, modern scopes have more than just empty space in the tube- but there’s nothing that alters the fact that locating the CCD about 160-200mm away from the objective lens produces a 1x intermediate magnification. In order to get a 2x magnification I would have to move the CCD an additional 160-200mm away from the objective lens (or use a relay lens like this).

As long as CCDs were small, everything worked out great- the small sensor size acted as an intermediate magnification (‘crop factor’), and so digital images looked similar to what you saw through the eyepiece. Because the CCD was located at the center of the image and the eyepiece magnified only the central part of the primary image, as long as the aberrations are well-corrected in the center, optical performance could drop at the field edges and nobody could tell. As sensor sizes have gotten larger, lens manufacturers have responded by coming out with lenses that are better corrected at larger and larger image heights. The c-mount specification allows reasonably sized images (22mm diameter), so as long as CCDs were less than 22mm in diameter all was well.

The result is that attaching a 35mm format sensor allows imaging of nearly the entire primary image, not just the central portion. Also, the 22mm-sized holes in the trinocular head restrict the image size to underfilling the sensor. The result is images that are suboptimal- only the central 1/4, at best, is useable.

Cue the ultraphot- this microscope, like Leica’s aristophot and Nikon’s multiphot, when used as a simple microscope has a bellows-type arrangement, resulting in a tube length that varies from (on the ultraphot) 880mm to 1200mm. The image circle at that distance is about 200mm in diameter (8 inches), reflecting the 6-8x secondary magnification that results from the long tube length.

Even better, I also enjoy a ‘crop factor’ of about 8, since my sensor size is so much smaller than the image. Now, a 40x objective appears to the camera as a 1900x-2500x zoom objective. Even my lowest magnification objective, a 4x, appears as a 200x lens. But nothing is free- what do I lose with these gigantic magnifications? Image sharpness due to diffraction. There are at least two approaches to correcting this problem.

One approach is to design special low-magnification lenses that also provide large image circles: macro lenses. Zeiss’s line is the luminar, Nikon’s is macro nikkor, and Leica’s is photar. These are surprisingly simple lenses- the luminars are cooke triplets. The optical performance of these lenses is astounding. Because the magnification is low (say 2x – 70x) the images are quite sharp.

The other way to try an restore image sharpness is to use high-NA lenses. Recall the maximum ‘useful’ magnification can be estimated as between 500 and 1000 times the numerical aperture. So, even though my magnifications can be large, if my numerical aperture is also large, I can restore the image sharpness.

Oh- I forgot to mention- the microsocope also has a 0.8x ‘focal reducer’ that does exactly that- reduces the magnification by 0.8x. Turns out, using that is required.

The optimal solution is a low magnification high numerical aperture lens. Like what, for example? Here’s some of our ‘favorite’ lenses we use in epi-illumination: 4x/0.1 epiplan, and 16x/0.35 epiplan. A quick calculation shows that the maximum useful magnification for these lenses, even with the focal reducer in place, is less than *half* the magnification obtained. The 16x lens in particular is a poor performer. How do the luminars perform? We primarily use the 100mm/0.08, epi-40mm/0.11, epi-20mm, and 16mm/0.2. The 63mm, while possibly our most-used lens, is easily substituted by the epi-40mm, resulting in considerably fewer part change-outs. The numerical aperture of the 20mm is unknown. The same calculation shows that the maximum useful magnification is nearly equal to the actual magnifications, resulting in sharper images. The ultraphot/aristophot/multiphot were designed with large-format (9cm x 12cm, 4″ x 5″) photography in mind, which also results in sharper prints (as compared with 35mm prints).

A 10x objective needs to have a numerical aperture of about 0.5, to provide pixel-limited (as opposed to ‘diffraction limited’, which is what we are trying to reduce!) images at the CCD. A 20x lens needs a numerical aperture of 0.95, and a 40x objective needs 1.5. Just for fun, a 100x lens needs a numerical aperture of 4.8. Clearly, we approach fundamental limitations very easily on the ultraphot! We searched the lab to see if we could find a lens that could provide higher magnification than the luminars, with numerical apertures that are as large as we could get.

Can we use infinity-corrected lenses? Don’t they need tube lenses? Not at the long tube lengths we are using- they might as well be infinitely long, as compared to 160mm and certainly compared to their focal length. And since we are cropping only the center 5% or so of the image, the aberration corrections performed by the tube lens (lateral color, spherical, etc) are not needed- we *really* obey the paraxial approximation!

Here’s a comparison, showing how much we have improved. The first image was one of the best using the ultraphot as a compound microscope- we used a 80x/0.95 with 2x optovar, and an additional 1.6x with an extension tube:

It’s not bad dead center, but field curvature throws the off-axis image out of focus rapidly. Plus, the image underfills the sensor. 250x is still much less than the maximum, about 600x. Now, here’s an image using the simple microscope optical path with a 40x/0.9 immersion lens:

The numerical aperture is the same, so there’s no additional detail, but notice that (1) the whole sensor is used, and (2) the image is sharp over the whole sensor. Finally, here’s the leica 100/1.47 oil:

Now there *is* some additional detail visible (although at a 1:1 display, the image is still blurry- damn you, wave nature of light!). The lenses we use now (besides the luminars) are leica 40/0.8 and 63/0.9 dipping and 100/1.47 objectives, a Nikon 20X/0.75 fluar lens, and a Zeiss 63/1.2 lens.

Ok, back to the images: Here’s how we can extract the maximum performance of an objective. We are going to first compare the 20/0.75 and 63/1.2- here are the two images:

We cropped the 20x to match the field of view of both images, and then down-sized the 63x image to match the image sizes, in effect de-magnifying the 63x image by about a factor of 3. Now, the effect of increasing the NA is clear- the 63x image has much more resolved detail.

Before I show a comparison between the leica 63x and 100x images, let me first note that the two previous lenses are close to 50 years old, and are finite-conjugate lenses. Ok, now see what 50 years of lens design gets us:

The differences are quite dramatic! What is especially impressive is that the 0.9 NA lens clearly outperformed the 1.2 NA lens. The difference in coloration is likewise impressive. This is why we love the 1.47 NA lens! We downsized the 100x only by a factor of two to achieve a good match between the pixel size and blur circle, so this image, when viewed at full resolution, is a magnification factor of about 1700, in good agreement with the maximum useful magnification for that lens.