Five degrees of separation

Last week, I carried on the quest for calibration. Avalon remains stubbornly out of reach. I tried things I mentioned last week and a new thing besides.

The liquid crystal device seems undamaged. To have a look, I improvised a light-table next to the confocal microscope. I put a flashlight inside a jar (otherwise used as our salad dressing cruet) pointing up, nestled in a bed of paper towels. With the flashlight on and Kleenex over the light, I put a linear polarizing filter on top of the jar, followed by the liquid crystal slider, arranged so that the optical axis of the first retarding crystal was at 45º to the transmission axis of the polarizer. I followed that by a second linear polarizer, with its transmission axis at right angles to that of the first one. I powered up the liquid crystals. Looking thru, I could see a unform color across the liquid crystal area (Figure 1). Changing the retardation of the crystals changed the color. There was no sign of a bleached out zone in the center or any other discontinuity. I am reassured that the unit is ok, although of course subtler kinds of damage might be present. 

Figure 1. Hastily snapped image looking through the liquid crystals. Note the uniform appearance of the light across the opening (Uh…actually the light might have saturated the phone’s camera but my own eyes were not saturated and detected no discontinuities). The small arc of discoloration to the lower left is because I was not able to hold the phone at a perfect right angle to the unit. 

 Next, I examined what happened when I immersed the objective to the polarizing filter with water. As I mentioned last week, the lens is designed to work be immersed to the slide and maybe immersion during calibration would reduce distortions to the state of polarization? The first way I tried this was with the same linear polarizer filter I used to check the liquid crystals. I used a region of interest while calibrating which is definitely the way to go. The calibration was tighter but not satisfactory, possibly because rotating this small square piece of plastic was a pain, especially to ± 45º. Then I noticed the rotatable polarizer that Rudolf Oldenburg lent me (along with the liquid crystal unit) could be immersed onto the lens. I repeated the calibration with his unit. The results were good but the calibration was still off, with the calculated orientation of the test object being ~5º out at each of the four test angles. 

Hmmm.  I removed the liquid crystal unit and measured transmission as a function of the angle of Rudolf’s linear polarizer (Figure 2). This has notches every 15º. I recorded the average intensity passing through the polarizer, restricting the measurement to a central region of interest. Because the laser is linearly polarized, the intensity is expected to vary as the cosine squared of the angle of the polarizer on the stage. I didn’t try a fit but by eye the curve looks appropriately steep. But the peaks and valleys are about 5º greater than 0, 90º, etc. Intriguingly, 5º is also about the error in the recent calibration. 

Figure 2. Transmission through a linear polarizer as a function of angle of its transmission axis. The unit was placed on the stage of the confocal and the light gathered by the condenser and passed to a detector. An angle of zero is parallel to the long axis of a microscope slide on the stage. As expected, the polarization direction of the laser is at ~90º; expected, because that direction is appropriate given the orientation of the dichroic mirror used to separate exciting and emitted light. 

There are two possibilities: maybe, the laser is mis-adjusted; or maybe, Rudolf’s rotatable polarizer was not quite orthogonal on the microscope stage. I favor the latter. Rudolf’s device is the length and width of a standard microscope slide; the rotatable bit is in the center. By eye, the unit looked well lined up; I did not check rigorously. It could have been aslant. 

Happily, I have another rotatable polarizer and one that locks onto the stage securely and precisely. But it has click stops only every 45º. Still, if the laser polarization is orthogonal to the stage, then the intensity at 45, 135, 225, and 315º (i.e., every 45º) should be the same. As evident in Figure 1, even a small misalignment causes the intensity to vary sharply at those angles, they are right in the middle of the ascending and descending arms of the curve. Thank you cosine. 

And just for grins (because all of this calibration biz puts such a large smile on my face) I am going to calibrate again with my rotatable unit. I used that originally but one reason why the calibrations might be getting sharper with immersion is simply because I am gaining practice. I’ll find out. 

Leave a Reply

Your email address will not be published. Required fields are marked *