www.photomacrography.net :: View topic - What exit pupil size for what aperture –DIY darkfield funnel

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zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

rjlittlefield

Joined: 01 Aug 2006
Posts: 19543
Location: Richland, Washington State, USA

 Posted: Thu Apr 28, 2016 5:13 pm    Post subject: Fan, I am not at all confident that I understand this problem. But since nobody else has responded, let me tell you my thoughts. First, by my understanding the stop diameter definitely should vary linearly with NA. I can't even make a good guess about why that is not the case with the adjustable objective you measured. Second, by my understanding it is always true that subject-side NA and camera-side NA are related simply by magnification, according to CameraSideNA = SubjectSideNA / magnification SubjectSideNA = CameraSideNA * magnification Third, for a finite system, the camera side NA is related to the stop diameter and distance from stop to image plane by the simple relationship that CameraSideNA = (StopDiameter/2) / DistanceFromStopToImagePlane As a cross-check on these relationships, we can consider the stop that you currently have. From your description, I get that: DistanceFromStopToImagePlane = 150 + 15 = 165 CameraSideNA = (3.05/2) / 165 = 0.009242 SubjectSideNA = CameraSideNA * magnification = 0.009242 * 65 = 0.60 This calculated value of 0.60 is slightly lower than the minimum value of 0.65 that is determined by your resolution measurement. The discrepancy is not large enough that I would rule out measurement error, especially given the difficulties that I've seen in measuring resolution even with simple subjects like ruled charts. But it is certainly enough to erode confidence in the calculation. Anyway, from the calculation alone, ignoring your measurement of 0.65
zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

 Posted: Thu Apr 28, 2016 6:36 pm    Post subject: Rik, Thank you very much! I feel fortunate to have your kind help. I think your calculation result of NA 0.6 makes more sense, based on your formulas and what I know about that darkfield funnel. That darkfield funnel was made for an 90x oil apo with original NA 1.4. I know for a fact that AO Spencer made darkfield funnel to stop down to DF NA of around NA 0.85. Going by your formulas and my mesurements on the LOMO objective (with slight length mismatch), that funnel would give 90x objective a DF NA of 0.83. That is probably as close as it can be to the factory setting of 0.8-0.85, considering the slight length mismatch. Using my mistaken estimation of NA 0.7, that funnel would give an impossibly high DF NA 0.97 for a 90x objective (they should not set it that high for general DF use). Even NA 0.65 estimation does not make sense either (DF NA 0.9 is still too high for a safe factory setting). My visual estimation of NA 0.65-0.75 was only based on diatom dot/line resolution, examined by my eyes, compared to NA 0.65 and NA 0.75 objectives. There was my psychological bias mistakenly favoring the 65x apo too (one side of my mind whispering to my ears "immersion apo should resolve better than dry achromat, stopped down or not"). Also, I was wrong for saying that my iris 30x NA 0.65-0.9 objective does not have stop diameter that varies linearly with NA. I confused half way of the iris wheel travel (which does not seem to produce a middling stop diameter) with a middling NA of 0.78. Have a great evening, Fan
rjlittlefield

Joined: 01 Aug 2006
Posts: 19543
Location: Richland, Washington State, USA

 Posted: Thu Apr 28, 2016 6:43 pm    Post subject: Excellent, this further information seems to resolve the inconsistencies that were bothering me. Thanks for the follow-up. --Rik
zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

 Posted: Thu Apr 28, 2016 7:02 pm    Post subject: Thank you so much, Rik. I apologize for the confusion caused by my mistaken estimation. Next time, instead of using subtle language like "it seems.....", I would just say " my likely mistaken guess is.........." That way, people would know not to take my guess seriously there.
rjlittlefield

Joined: 01 Aug 2006
Posts: 19543
Location: Richland, Washington State, USA

 Posted: Thu Apr 28, 2016 7:57 pm    Post subject: No worries! I think I understood the situation pretty well, and it wasn't like I was agonizing over the discrepancy. If you're looking for a more neutral phrase, perhaps something like "by visual estimation" would convey less certainty without going all the way to self-deprecation. --Rik
zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

 Posted: Tue May 03, 2016 1:20 pm    Post subject: My machinist friend has been busy, so I did an experiment to compare the effect of stop location on darkfield image quality. I made a rear disc diaphragm myself, out of aluminium sheets, to stop down a 40x NA 0.95 apo objective to around NA 0.82, at 145 mm from image plane. The NA 0.82 turned out to be a good comprise between NA 0.95 and NA 0.65, as it significantly reduced (out-of-focus) halos of the NA 0.95 and provided better resolution than NA 0.65. The alternative way to place the stop is using a funnel stop at around 165 mm from image plane. Rik told me that this placement may produce better image, as more of the lens center is utilized (than the 145 mm placement). Unfortunately, my 40x NA 0.95 objective has an complex internal structure and does not allow internal funnel. Although my water immersion 65x NA 1.1 objective can accept internal funnel, which we are going to make. As a side note, the magnification in Rik's formulas refers to only objective magnification, so eyepiece magnification does not matter for those formulas. I will update this thread, once we make and test the funnel stop.
zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

 Posted: Tue Jun 21, 2016 2:27 pm    Post subject: My machinist friend made me those darkfield funnel stops, based on Rik's calculations/formula. Everything works very well! Using those custom darkfield stops and mounted diatoms, I can visually see the difference between immersion objective NA 0.87 vs NA 0.95, and dry objective NA 0.95 vs NA 0.85. Difference is there, though not a lot. Difference is more significant between immersion objective NA 0.87 vs NA 1.1. If any microscopist wants to make similar custom darkfield stops, (s)he can message me and I will refer my machinist friend to you. I suggest reading this thread yourself and come up with the exact stop diameters though, before contacting my friend (he is not a microscopist)._________________Selling my Canon FD 200mm F/2.8 lensLast edited by zzffnn on Sat Jun 25, 2016 9:46 am; edited 1 time in total
rjlittlefield

Joined: 01 Aug 2006
Posts: 19543
Location: Richland, Washington State, USA

 Posted: Sat Jun 25, 2016 9:43 am    Post subject: This is good to hear. Thanks for reporting on the final result. --Rik
zzffnn

Joined: 22 May 2014
Posts: 1700
Location: Texas USA

 Posted: Sat Jun 25, 2016 9:57 am    Post subject: Thank you, Rik. You can count on me on reporting back results. I always consider that my responsibility, once I ask a question and get an answer/advice. I have seen people who wrote down a question then disappeared - I cannot say I like that._________________Selling my Canon FD 200mm F/2.8 lens
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