J. Kissel

Executive Summary
I've tuned the lens position and measured the projected beam profile of one of three trial fiber collimators to be used for the SPI. The intent is to do this measurement before vs. after a vacuum bake like done for previous collimators (Section 3.3 of E1500384), to see if the bake will cause any negative impact on the performance of the collimator. It also helped clear out a few "rookie mistake" bugs in my data analysis, though there's still a bit of inconsequential confusion in post-processing the fit of the beam profile.

Full Context
The SPI intends to use supposedly vacuum compatible Schaefter + Kirchhoff (SuK) fiber collimators (D2500094, 60FC-0-A11-03-Ti) in order to launch its two measurement (MEAS) and reference (REF) beams from their fiber optical patchcords attached to feedthroughs (D2500175) in to free-space and throughout the ISIK transceiver / interferometer (D2400107). However, unlike their (more expensive) stainless steel counterparts from MicroSense / LightPath used by the SQZ team, SuK doesn't have the facilities to specify a temperature at which they believe the titanium + D-ZK3 glass lens + CuBe & Ti lens retaining ring assembly will fail (see E2300454). As such, we're going to run one SuK collimator through the same baking procedure as the MicroSense / LightPath (see Section 3.3 of E1500384) -- slow 6 [hr] ramp up to 85 [deg C], hold for 24 hours, similar slow ramp down -- and see if it survives.

A catastrophic "if it survived" result would be that the lens cracks under the stress of differential heating between the titanium, CuBe, and glass. 
As we don't expect this type of failure, in order to characterize "if it still functions," we want a quantitative "before" vs "after" metric. 
Since I have to learn how to "collimate" this type of collimator anyways (where "collimate" = mechanically tune the lens position such that emanating beam's waist is positioned as close to the lens as possible), I figure we use a 2D beam profile as our quantitative metric. We expect the symptom of a "failed" fiber collimator to be that "before bake it projects a lovely, symmetric, tunable, Gaussian beam, and after bake the profile looks asymmetric / astigmatic or the lens position is no longer consistently/freely adjustable."

The SPI design requires a beam whose waist (1/e^2) radius is w0 = 1.050 mm +/- 0.1 mm. That puts the Rayleigh range at zR = pi (w0^2) / lambda =  3.25 [m], so in order to get a good fit on where the waist lies, we need a least one or two data points beyond the Rayleigh range. So that means projecting the beam over a large distance, say at least ~5-6 [m].

Measurement Details
2025-06-03_SPIFC_OpticalSetup.pdf shows the optical setup. 

Pretty simple; just consuming a lot of optical table space (which we thankfully have at the moment). The "back" optical table (in IFO coordinates the "-X table (with the long direction oriented in the Y direction") already has a pre-existing fiber coupled, 1064 nm, laser capable of delivering variable power of least 100 [mW] so I started with that. It's output has an FC/APC "angled physical contact" connector, where as the SuK fiber collimators have an FC/PC (flat) "physical contact" connector. I thus used a ThorLabs P5-980PM-FC-2 APC to PC fiber patch cord to couple to the SuK fiber collimator, assembled with a (12 mm)-to-(1 inch) optic mount adapter (AD12NT) and mounted in a standard 1" mirror mount, set at 5 inch beam height. Ensuring I positioned the free-space face of the collimator at the 0 [in] position, I projected to beam down the width of the optical table, placed steering mirrors at 9 [ft] 9 [in] (the maximum +Y grid holes), separated by 6 [in] in order to return the beam down the table. Along this beam, I marked out grid-hole positions to measure the beam profile with a NanoScan head at 
    z = [0.508 0.991 1.499 2.007 3.251 4.496 5.41] [m] 
These are roughly even half-meter points that one gets from "finding 1 inch hole position that gets you close to 0.5 [m] increments", i.e. 
    z = [1'8", 3'3", 4'11", 6'7", 10'8", 14'9", and 17'9"].

Using the SuK proprietary tooling, I then loosened the set-screws that had secured the lens in position with the 1.2 mm flat-head (9D-12), and adjusted the position of the lens with their short eccentric key (60EX-4), per their user manual (T2500062 == Adjustment_60FC.pdf), with the NanoScan was positioned at the 5.41 [m] position.
At the 5.41 [m] position, we expect the beam radii to be w(z=5.41 m) = w0 * sqrt(1 + (z/zR)^2) = 2.036 [mm], or a beam diameter of d(z=5.41 m) = 4.072 [mm].

Regretfully, I made the rookie mistake of interpreting the NanoScan's beam widths (diameters) as radii on the fly, and "could not get a beam 'radii' lower than 3.0 [mm]," at the z = 5.41 position, as adjustments to the eccentric key / lens position approached a "just breath near it and it'll get larger" level at that beam size. This will be totally fine for "the real collimation" process, as beam widths (diameters) of 4.0 [mm] required much less a delicate touch and where quite repeatable (I found, while struggling to achieve 3.0 [mm] width).

Regardless, once I said "good enough" at the lens position, I re-secured the set screws holding the lens in place. That produced a d = 3.4 [mm] beam diameter, or 1.7 [mm] radius, at the z = 5.41 [m]. I then moved the NanoScan head to the remaining locations (aligning the beam into the head at each position, as needed, with either the steering mirrors or the fiber collimator itself) to measure the rest of the beam profile as a function of distance.

2025-06-03_SPIFC_BeamScans_vs_Position.pdf shows the NanoScan head position and raw data at each z position after I tuned the lens position at z = 5.41 [m].
Having understood during the data analysis that the NanoScan software returns either 1/e^2 or D4sigma beam *diameters*, I followed modern convention and used the mean D4sigma values, and converted to radii with the factor of 2, w(z) = d(z) / 2. One can see from the raw data that the beam profile at each point is quite near ''excellently Gaussian,'' which is what we hope will remain true *after* the bake.

Results

2025-06-03_spifc_S0272502_prebake_beamprofile_fit.pdf shows the output of the attached script spifc_beamprofile_S0272502_prebake_20250603.m, which uses Sheila's copy of a la mode to fit the profile of the beam.

Discussion
The data show a pretty darn symmetric beam in X (parallel to the table) and Y (perpendicular to the table), reflecting what had already been seen in the raw profiles.
The fit predicts a waist w0 of 
        (w0x, w0y) = (0.89576, 0.90912) [mm] 
at position 
        (z0x, z0y) = (1.4017, 1.3469) [m] 
away, downstream from the lens. Makes total sense that the z position of the waist is *not* at the lens position, given that I tried to get the beam as small a *diameter* possible at the 5.41 [mm] position, rather than what I should have done which is to tune the lens position / beam diameter to be the desired 4.072 [mm].

What doesn't make sense to me, is that -- in trying to validate the fit and/or show that the beam behaves as an ideal Gaussian beam would -- I also plot the predicted beam radius at the Rayleigh range, 
    w(zR) [model] = w0 * sqrt(1 + (zR/zR)^2) = w0 * sqrt(2),
or 
         (wzRx, wzRy) [model] = (1.2668,1.2857) [mm]
which is much larger than the fit predicts,
         (wzRx, wzRy) [fit] = (0.9677,0.9958) [mm]
at a Rayleigh range,
    zR = pi * w0^2 / lambda
of 
         (zRx,zRy) [from fit w0] = (2.3691, 2.4404) [m]

Similarly confusing, if I plot a line from the waist position (z0x, z0y) to the end of the position vector (6 [m]), whose angle from the x-axis is the divergence angle
    theta_R = lambda / (pi * w0)
i.e. a predicting a waist radius at zEnd = 6 [m] of 
    w(zEnd) = (zEnd - z0) * atan(theta_R)
this results in a beam waist at xEnd much smaller than the fit. Most demo plots, e.g. from wikipedia:Rayleigh_length or wikipedia:Beam_divergence, show that slope of the line should start to match the beam profile just after the Rayleigh range. To be fair, these demos never have quantitative axes, but still. At least the slope seems to match, even though the line is quite offset from the measured / fit z > 6 [m] asymtote.

Conclusion
Though I did not adjust the lens position to place the beam waist at desired position, I now have a good measurement setup and data processing regime to do so for the "production" pair of fiber collimators. For this collimator, since we're just looking at "before" vs. "after" bake data, this data set is good enough.

Let's bake!