March 12, 2022
While successful, implementation of collimated beam projector to date has two issues: 1) dynamic range mismatch between monitor diode (wants nA of current) and astronomical instrument (100,000 electrons per pixel max), and 2) not directly monitoring beam at exit pupil, due to size mismatch.
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Note that this is also somewhat dispersive, which is actually a plus.
Source needs to be on-axis for spherical reflector, otherwise we get off-axis aberrations (coma, in partticular).
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It's also useful to move solar cell further back so its surface reflections don't bounce back from lens backside.
different reflection orders for 3 inch diameter beam are separated by 0.1*L a distance L from the wedge.
What about using a positive meniscus lens, one side for reflective collimator and other side to focus onto photodiode?
For spherical reflector, focal length is R/2.
For lens of index n, 1/f=(n-1)*(1/R1 + 1/R2)~ 0.5(1/R1+1/R2). So for n=1.5, the transmissive and reflective focal lengths are the same, for plano-convex or plano-concave lens. So if source is at the focus, both reflected and transmitted beams are collimated. Huh.
NBK7 index is 1.5168
Fused Silica index is < 1.5 for lambda > 275 nm. So concave-convex FS lens has 1/f=(0.47)(1/r) and f=2.12 R.
Desired attenuation
Imagine we want nA of photocurrent in monitor diode, and (spread over 100 pixels) 100*100,000 in 10 sec = 1e6 emitted photons/sec.
For unity QE that is photon rate on diode of 1e-9 Coul/sec * 1 e/1.6E-19 Coul = 6e9 photons/sec. That's an attenuation of 6000.
For 4% reflection here is attenuation vs number of bounces:
n=1 n=2 n=3 n=4
25.0000e+000 625.0000e+000 15.6250e+003 390.6250e+003
So n=3 looks favorable. How much flux? the unattenuated beam is 6e9 photons per sec. At 1E-19 joules per photon we want 6e-10 Watts so nW of power.
That should be OK....
A more elegant implementation:
Considerations-
Stray light is going to be the main issue. Wavelength dependence of collimated vs. off-angle light introduces a systematic error.
Need to rotate the axis of reflection each time, to balance out polarization effects upon reflection.
best to keep angle of incidence below 10 degrees.
From https://refractiveindex.info/?shelf=glass&book=BK7&page=SCHOTT
At 808 nm:
| angle (degrees) | Rp | Rs |
|---|---|---|
| 0 | 0.041365 | 0.041365 |
| 5 | 0.040948 | 0.041784 |
| 10 | 0.039693 | 0.043069 |
| 15 | 0.037593 | 0.045301 |
| 20 | 0.034640 | 0.048630 |
If angle of incidence is 10 degrees, reflected beam rotates by 20 degrees. If beam of diameter D rotates by theta, distance it must travel to not have incident and reflected overlap obeys tan(theta)=D/L so L/D=1/tan(theta)
| theta_incidence | theta_refl | L/D |
|---|---|---|
| 5 | 10 | 5.7 |
| 10 | 20 | 2.7 |
| 15 | 30 | 1.7 |
Purchases
Lambda optics 2 inch concave mirror blanks, polished both sides.
Your Lambda Research Optics order has been received.pdf
Bought some 6 inch aperture concave optics on eBay.
Bought Omegon 203mm aperture, 2436mm collimator. A 100 micron diameter fiber subtends an angle of 100E-6/2.436 radians = 8.5 arcsec.
Beam is f/12. Back focal length from flange is 23 cm, from focuser is 14 cm. Allowable aperture for 2 arcsec diffraction limit (so it is subdominant relative to geometrical optics)
is 10E-6=400 nm/D do D > 400e-9/10e-6 => D> 40mm so 2 inch (50mm) optics should be fine.
f*lambda is 12*0.5 microns = 6 microns. Launcher could be 10 micron pinhole in front of fiber. Or a 10 micron multimode fiber?
Also bought wedges on eBay, > 2 inches in size.
Feb 2023 Design
HgAr source, 12V 3W so around 500mA@12V:
Beam source
either tunable laser or else modulated photodiodes. If we want a 10 micron spot at f/12, need to inject the input beam at slow f/# as well.
a 50 micron fiber needs to be 12*50 = 600 microns away from a pinhole to generate an f/12 beam.
Disperser
Say we want adjustable dispersion with Risley prism arrangement. At n1sin(theta1) = n2sin(theta2). For small angles we get 1.5*theta1=theta2. deflection is theta1-theta2 = theta1-1.5 theta1 = theta1 *(1-n(lambda)).
Using https://lightmachinery.com/optical-design-center/more-optical-design-tools/prism-designer/
| apex angle | incidence angle | 300 nm angle | 1100 nm angle | difference |
|---|---|---|---|---|
| 1 | 1 | 0.487 | 0.449 | 2.2 arcmin |
| 1 | 10 | 0.4981 | 0.4589 | 2.35 arcmin |
| 10 | 5 | 4.904 | 4.523 | 22.86 arcmin |
This wedge pair needs to be tilted relative to incident beam. Five degree wedge angle seems good, as a pair. That gives us variation from zero to around 30 arcmin. For any sensible focal plane array of 4K x 4K
Jan 31 2024 CWS
light source conceptual design
If we use a laser-driven Xenon light source, from Energetiq (we have one in lab, in a box) we get this output spectrum: (https://www.energetiq.com/eq99xfc-fiber-coupled-broadband-light-source)
If we operate with spectral bandwidth of around 1 nm, with a 200 micron diameter fiber we get around 10 uW/nm of spectral density. That would generate around 5 uA of photocurrent in photodiode, that's a lot! Even with factor of one hundred loss in transmission to photodiode we should be fine.
Possible double monochromator: https://www.spectralproducts.com/CM112/2232
they claim 1 nm bandwidth with 150 micron slit. Needs external order-blocking filter though, for lambda > 550 nm. Monochromator is f/3.9, laser driven light source is unknown.
notional system diagram:
References
Large optical wedge vendor, example: https://www.precisionoptical.com/precision-optics/optical-flats/unmounted-reference-flat/
plano-concave high quality mirror blanks, up to 50mm diahttps://www.lambda.cc/product/plano-concave-mirror-blanks-pccm/
polarization-preserving configuration with 4 reflections ol-26-13-971.pdf; (Galvez, E. (2001). Achromatic polarization-preserving beam displacer. Optics Letters, 26(13), 971–973. https://doi.org/10.1364/OL.26.000971)
We note the reflective designs in this paper which document a 4-element system that adequately* preserves the initial polarization / phase of light.
| title | link | |
|---|---|---|
| Theory of the optical wedge beamsplitter | The_Theory_of_the_Optical_Wedge_Beam_Spl.pdf | |
| Achromatic polarization-preserving beam displacer | https://doi.org/10.1364/OL.26.000971 | |