Reflective Attenuated CBP (RACBP)

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. 

A reflective design can take advantage of the known index of refraction of glass to have a good theoretical value for attenuation. Typical uncoated optics reflection is around 4%. 

We can estimate how much attenuation we need by comparing the integrating sphere areas aubtended by output aperture and monitor diode. Full optical fiber input energy is distributed on surface of 2 inch diameter integrating sphere. Area is 4piR^2, or 8.1e3 square mm. For a 10 micron output pinhole, fraction of energy that emerges is A1/A2 = pi*2.5e-3^2/A2 = 2e-5/8e3 ~ 2.5e-9 of optical fiber energy. Wow and ouch. 

ratio of photodiode area to pinhole area is (5mm/5 microns)^2 ~ 1e6.

When we run current CBP with 5mm output aperture, photodiode to aperture ratio is about 1:1. 

For 200 micron fiber to subtend 1 arcsecond, we need a focal length of at least 200e-6/FL=5e-6 so FL=40 meters. That won't work!

Use 10 micron pinhole, need 10e-5/FL = 5e-6 so 2 meter focal length. A telephoto configuration is then 1m long. Sounds OK. 

Assume beam we need is around f/10, that means 200 micron fiber needs to be 2mm away from pinhole. That would be fairly efficienct, compared to existing configuration. 

CVI laser makes UVFS 3 inch diameter wedge with 3 degree angle. Successive-reflection beams on same side emerge 6 degrees apart, with slight displacement. Sin(6 deg) = 0.1, so for 1m length the separation is 10cm = 4 inches. That's about right!. The Thor Labs rectangular beamsplitting wedge is 5 degree angle.

spherical aberration is tolerable as long as beam is slower than about f/8. If we design for f/10 then this ought to work well 

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). 

Radius of spherical side of Plano-convex lens has to be 3 inches more than radius of meniscus lens. Maybe we just do away with that, and the whole thing is long?

Diffraction limit for 3 inch output beam is 1.3 arcsec at 500 nm. for 75mm footprint on reflector, and 2m focal length, f/number is 75/2000 = 27. So diffraction-limited spot at 500 nm is 0.5 microns * 27 = 12 microns. Good match to 10 micron pinhole. 

If we eliminate the meniscus lens, the reflector only needs to be twice the beam size, or 6 inches in diameter. 

We could bond a wedge to back of plano-convex lens to send second reflection off in a different direction. 

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: 

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)

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/

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: 

RACBP Spring 2024 Parts List:

We note the reflective designs in this paper which document a 4-element system that adequately* preserves the initial polarization / phase of light.

Status updates: 

An initial version of the RACBP was constructed in the benchtop lab setup on Feb. 22.

Initial testing with a 532nm laser unfortunately showed strong and tightly spatially located double-bounce propagation through the system, indicating that the 30-arcmin wedge on the wedge windows purchase would be insufficient for canceling double-bounce issues. 

Consequently, plano-convex lenses of the fastest f-ratio were ordered and installed the following week as replacements to the wedge windows; initial observation reveal that this modification  appears to successfully cancel out double bounces, representing a step closer to taking controlled flux measurements through the system at this proof-of-concept stage. 

In-progress/next steps: finalizing modelling results for system ; angular alignment tolerance, verification of polarization effects. 

Reworking physical layout and installing double monochromator system and operation with expanded beam profile. 

(Galvez, E. (2001). Achromatic polarization-preserving beam displacer. Optics Letters, 26(13), 971–973. https://doi.org/10.1364/OL.26.000971)

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