well… since bulldogging thru, worked this good so far? might as well go with THAT for this session… no sense wasting being in the zone…
QUOTE
2 Aspheric lens pairs
A second aspheric lens can be added in front of the collimating lens
to focus the light over a desired area. The illuminated
spot diameter at the focal plane (FP) is given by:
ENDQUOTE
well? we can do THAT now, if everything else was correct… screw it…
spot diameter = DIAMsource * (Ffocus / Fcol)
spot diameter = ? well, we know if nothing else, the diameter of the source, thats 1mm, right?
spot diameter = 1mm * (Ffocus / Fcol)
=
we got half of this, anyways… the spot diameter is 1mmTIMES THE RATIO, and a real nice number. more importatly? the millimeters inthe ratio will cancel out wharever they are… the answer is in millimeters, left over last unit from the 1mm source diameter, after canceling out?
million… dollar… question….
what freaking ratio? we are 1.5 equations away, from walking on water… i only know,i got the tiger by the tail and dont wanna lose it…
okay… stop… think??? we can SET the spot diameter after the lens pair? to be whatever we WANT it to BE…just, what do we ant it to BE?
uhmmmmmm. in the LAST one lens zoomie math model? using “best lens scenario”, above which the extra lens power is “useless” as the entire set of “rays” escaping the waiven collar is captured mathemastically? what more is there to “gain” than THAT?
okay… lets “go with that” assumption… we only GOT THAT optimum setup? simply because we used a waiven collar, which fired up the emitter hyper, and contained an escape angle of 60 full, 30 above the x axis… right?
so… maybe, and i mean just maybe? this portion is reserved for “getting optimum” assuming we DIDNT use the waiven collar? that we COULDNT find a suitable lens with the proper stupid numerical aperture… which is simply the F-number hiding under an assumed name…
so… we… what? we want to SET THE RATIO so as… to accomplish this, assuming we NEEDED To.???
i’m thinking out loud…. i am talking myself into this line of thought… we are only stuck here, simply because we are ALREAY capable of finding lenses that are “optimum capture angle” already with the one lens model.
what if we WERENT ABLE TO be “here”? which is any time without THIS special emitter, without THIS special case of using a waiven coller… we WOULD want to “be here” regardless, right???
and… setting THAT RATIO, will PUT us where we want to “be”.
=
okay, i talked myself into it…. i am forgetting the whole single lens zoomie workup? that was just an academic exercise to get me HERE, working with THIS portion…
go back, see “what” was optimum about that setup…we RE-make it HERE, with this stupid ratio?
shrugs i like the logic train of it….
houston, we have a problem… we never calculated a “spot diameter” back there… all we calculated was a “beam diameter”. is that the same thing? engineer dont use terminology lightly… whatever the differenc ebetween a beam and a spot “is”? it might mean something… of course, it could also just be a convention based on whether you use one lens or two lenses.
decisions… decisions… decisions….
also? any clue i take from the previous session? is “switching backwards”… if i like to think of calculating this spot diameter, as the same as the beam calculation previously? the one lens collimated beam diameter, was the 2NA*Fcol equation… here? its “more like” the previous divergence formula… and my next equation, also containing this holy ratio we set? is switching the collimator/focus ratio upside down… its a reciprocal… and, thats the divergence equation in THIS section, looking more like the other equation back there…
what to do?
okay…. pondering the pnderables? lets say maybe the spot diameter and the beam diameter arent the same thing… i dont know… BUT, i am just bout to calculate the divergence, and while the equation is way different than last time? a term is a term… divergence is… divergence.
since i am trying to assume that we couldnt set divergence “optimum” and now would be our chance to do it? we couldnt get the cool lens we had for optimum last time? then i want my divergence set to “optimum” we got lucky and HIT optimum in the single lens, maybe i can use that as an “answer” then solve for the ratio i want? that will produce it?
its a thought… well, thats one variable out of the way… i need ONE of those ratios to be set for me…
hmmm. maybe we COULD use the “single lens” optimum, use that as the bigger forward focusing lens? i mean, lets not waste it… thats another variable down… where we at in the second equation? if i can SOLVE for the ratio last need, i will have the ratio to plug into the previous equation?
scrtew it, lets try that…
the optimum theta divergence, only because we HAD an attainable lens? WAS an answer of… ehat was it?
optimum radians? WAS 1 / 86.6…
so…
(1mm / 86.6mm) = 2 * NAbeam * (ratio)
mm’s cancel out…
.011547344 = 2 * NAbeam * ratio
.011547344 = 2 * .5 * ratio
.011547344 = 1 * ratio
BUt, following this line of thought? ratio = reusing the cool lens, as the “forward focus lens”?? equals 86.6 as the bottom of the ratio…
.011547344 = 1*(Fcol/86.6)
? eh
now, need the “new” collimating lens, to be… smaller than the focusing bigger lens… which is 86.6…. if i solve this, i might get the focal length of the new collimating lens, hat used with this lens, would make the optimum lens setup, assuming i didnt already have it available with one lens previously… hmmm, watch this give me a nonsensical answer, LMAO
1 times anything is anything, i am left woth…
.011547344 = Fcol/86.6
.011547344 times 86.6 = Fcol?? try it…
i get “1mm” as the proper focal length of the collimating lens….
wait a minute! that actually might make sense!
since we already HAVE the “optimum one lens”, and i was using that radians answer to derive the rest of the ratio? it is stating that the “ratio” is already set up? maybe?
okay… thats either nonsense, or it means maybe what i think it might mean… lets try this… with… a “lesser lens” and solve for the same radians answer, the optimum we already know from the one lens example…
maybe i can “hit it” based on any focal length lens i CHOOSE to use for the focuser? okay, lets se what it would be for… a 100mm FL focusing foreard lens… nice round number…
.011547344 = 1*(Fcol/86.6) scratch that….
.011547344 = 1*(Fcol/100)
1 times anything is anything
.011547344 = (Fcol/100)
.011547344 = fcol/100
multiply both siddes by 100, duh…
1.1547344 = Fcol
heck, a ratio is a ratio, right? lets fire this puppy in with a… 600mm forward focusing lens… we’re just setting a ratio, right? maybe THAT will get the focusing collimator up into something reasonable to fiond in a col. lens??? worth a shot. i can create a ratio out of thin air like this… and i can still run any ratio back up thru the “spot diameter” equation see what it spits out…
.011547344 = 1*(Fcol/100) scratch that… bigger number, to get a realistic collimator mm fogure…
.011547344 = 1*(Fcol/600) now we’re either totally lost? or were cooking with gas…
.011547344 = (Fcol/600) cos 1 times anything is anything…. multiply both by 600?
NOW i get Fcol = 6.9284064 = 6.3mm collimating lens
THATS more realistic…. to “find”… in asmall collimator…
=
i am NOT calling this solved? i’m saying this is a possibility….
just, let me feed this “600 ratio” back into the above equation? see what he spot diameter is… maybe it will be similar to the “optimum” one lens beam diameter was? i am either close or done? or completely lost…
spot diameter = DIAMsource * ( 6.9284064 / 600) source diameter always was 1mm…
spot diameter = 1mm * (.01157344)
spot diameter = .01157344
does that even make sense??? check it… look for it…
HEY!!! i got rthe SAME RADIANS!!! witha totally different equation!!!
==
i’m am NOT calling this solved? i am just calling this… best whack i ever took at it…
someone suffer thru this logic trainwreck see what i might have had abrain fart? or else… i am a golden god? (and i just cant be… i aint that smaert… there has to be a monumental logic *&%$ up… this is way above mypay grade…)
still… i got “something” working… sort of? pinch this off, before i hit a bad key and lose all this work…