J. Kissel

Executive Summary
Using 
   - the AxcelPhotonics butterfly diode laser,
   - the "beam splitter / near-field / bypass" measurement setup described in LHO:89123 to rapidly check the beam diameter at z = 0.991 [m] (near field) and z = 5.41 [m] (far field), 
   - elevating the beam height elevated to 5 [inches] to avoid any sort of clipping on other optomechanical setups on the table from other teams, and
   - loosening the lens position set screws only just barely, 
   - paired fiber collimators, in-vac feedthrus (with integrated patch cords), and ex-vac 7.5 m patch cables in-vac feedthrus 

      Beam Path   Char Date    Collimator   Feedthru (Pwr Transmission*)
      MEAS        2026-02-13   S0272503     S3228003 (100%)    
      REF         2026-02-17   S0272502     S3228002 (99%)    

      * Power transmission as reported from SWG:12296

I was "rapidly" tune the lens position, z_lens, for *both* the MEAS S0272503 and REF S0272502 fiber collimators to within 0.010998 (i.e. 11 [mm] - 2 [um]) with uncertainty of +/- 1 [um] , such that 

each fiber collimator sends out a free-space beam whose parameters meets SPI's requirements:
   - the desired waist radius (in both x/y dimensions) , w0 = 1.05 [mm], of within +/- 0.10 [mm], and
   - the desired waist position (in z), z0 = 0.0 [m] to within +/- 0.18 [m].

(where "rapidly" is in quotes: about 4 hours each from "install into measurement setup" and "I'm happy with a final full-position-vector scan). with no signs of strong astigmatism that I saw in the initial setup. (The later point confirms my suspicion that I was clipping on the EOM characterization setup, and there is *no* issue with the laser seed mode, polarization, or the beam splitters).

Support Media

The raw data from the beam profiles of each free-space beam are posted as
    2026-02-17_spi_fc_S0272502_ft_S3228002_7p5mPatchCord_AxcelPhotonicsLaser.txt
    2026-02-13_spi_fc_S0272503_ft_S3228003_7p5mPatchCord_AxcelPhotonicsLaser.txt

where the columns are jammt-friendly format of z Position [cm], Y waist radius [um], X waist radius [um]. 

Notes: 
    (1) as opposed to all previous data sets (e.g. LHO:89047, LHO:86350, LHO:84825) -- I added an additional measurement at z = 0.25 [m] to try to improve the accuracy of the fit beam.
    (2) X is "Axis 1" of the NanoScan parallel to the optical table, Y is "Axis 2," perpendicular to the table. As discussed in LHO:89099, jammt seems to import any three-column dataset such that the first column ends up fit as the "tangential w0," and the second column end up fit as the "w0." With a la mode, the data is typed in a matlab script manually, so X and Y data are modeled separately the entire time without rename, and thus kept consistent. Thus the intentional flip the X and Y axes in the text file such that a la mode and jammt are now both treating w0 = X = Axis 1 = parallel to table, and tangential w0 = Y = Axis 2 = perpendicular to the table.

I imported these beam profiles into both matlab (to run a la mode) and jammt to obtain waist radius, w0, and waist position, z0, fits to the AxcelPhotonics beam profiles, see attached plots:
    S0272502  a la mode  jammt
    S0272503  a la mode  jammt

Some pictures of the measurement setup with the NanoScan head at the new z = 0.25 [m] position (upstream of the beam splitter bypass):
    2026-02-13_FC_S0272503_S3228003_MeasSetup.jpg
    2026-02-17_FC_S0272502_S3228002_MeasSetup.jpg

Some pictures of the clean fiber collimator + vacuum feedthru systems packed up after measurement:
    2026-02-13_FC_S0272503_S3228003_PackedUp.jpg
    2026-02-17_FC_S0272502_S3228002_PackedUp.jpg

Detailed Analysis Results

Here's a table of the fit results from both a la mode and jammt. 


        

            

                
FC + FT S/N
Model
w0x [m]
z0x [m]
w0y [m]
z0y [m]
            
        
        

            

                
S0272502 + S3228002
a la mode
1.0392
-0.065196
1.0427
-0.020038
            
            

                
jammt
1.0392
-0.06521
1.0427
-0.02007
            
            

                
S0272503 + S3228003
a la mode
1.0396
+0.17704
1.0282
-0.030537
            
            

                
jammt
1.0396
+0.17702
1.0282
-0.03051
            
        
    
It's not a typo, the two fitting softwares agree to within the precision of the each display; +/- 10 [um] on both the waist radius and waist position.

From here on in this section, since I intentionally paired up fiber collimators and fiber feedthrus to match the last two digits of serial number, I'll refer to them as either "MEAS = S[...]03", or "REF = S[...]02".

From the table of fits, you see that the statement in the executive summary about the waist position, z0 = 0.0 +/- 0.18 [m], is defined expanded to cover the X axis waist position of MEAS = S[...]03 z0x = +0.177 [m]. But really, the other axis of the MEAS = S[...]03 FC+FT pair is at z0y = -0.031 [m], and the REF = S[...]02 FC+FT pair is within z0x = -0.065 [m], and the best z0y = -0.020 [m].
So the waist positions are really *quite* close to 0.0 [m]. 

Good. So let's use these numbers to do recast the fit (using jammt numbers only) into context:
    (1) Percent Difference between desired waist radius and final measured waist radius:

        REF, S[...]02 :: (w0x, w0y) = ([1.0392 1.0427] - 1.05) / 1.05
                                    = [-0.0102860  -0.0069524] 
                                    = [-1.0% -0.7%]
                    Within 1.050 +/- 0.1 [mm] = 1.050 [mm] +/- 9.5 [%] = [1.15 0.95] [mm]?
                    Both axes waist radius are a factor of 10x better than reqs.
        MEAS, S[...]03 :: (w0x, w0y) = ([1.0396 1.0282] - 1.05) / 1.05
                                     = [-0.0099048  -0.020762] 
                                     = [-1.0% -2.1%]
                    Within 1.050 +/- 0.1 [mm] = 1.050 [mm] +/- 9.5 [%] = [1.15 0.95] [mm]?
                    Both axes waist radius are a factor of 5x better than reqs.
        

     (2) Rayleigh Range:  

         (zR := pi * w0^2 / lambda)

         REF, S[...]02 :: (zRx,zRy) = (3.1886, 3.2102) [m]
         MEAS, S[...]03 :: (zRx,zRy) = (3.1911, 3.1215) [m]

         There's no requirement on where the Rayleigh range sits, but for a waist radius of w0 = 1.05 [mm], we would expect a Rayleigh Range of zR = 3.255 [m], and these values are at most z = -13 [cm] from that or 4% "short" of the target value. This doesn't really matter to SPI, as long as the Rayleigh Range is somewhere in between the ISIK breadboard and the ISIJ reflector 15.427 [m] away. The real requirement is the spot size at the ISIJ reflector, which we need to keep at the design value of 5 [mm] (whose value was determined with the original design waist radius of 1.05 [mm], and the acceptance that we didn't have enough room on the ISIK transceiver breadboard to install telescopic lens solutions to keep the spot size around 1 [mm] both within the transceiver *and* at the ISI reflector). 

      (3) Astigmatism: 

          A := (zRx - zRy) / (zRx + zRy)

          REF, S[...]02 = -0.003376 = -0.3%
          MEAS, S[...]03 = +0.011026 = +1.1% 

          Here, again, there's been no requirement on the astigmatism, but ~1% astigmatism doesn't smell too terrible. 

      (4) Spot size at 15.427 [m]: 

          w(z) = w0 * sqrt(1 + (z/zR)^2) 

          REF, S[...]02 :: (x,y) = (5124.569, 5155.038) [um]
          MEAS, S[...]03 :: (x,y) = (5194.496, 5075.909) [um]

          Recall the design value of waist radius at the ISIJ reflector, z = 15.427 [m], is w(z = 15.427) = 5 [mm]. As discussed in SWG:12273, that ADC noise with the large spot size is limiting the sensitivity of the pitch and yaw readout, as 

          dx/dTheta ~ sqrt(8/pi) L / w(z).
    
          But still, a 1.1% level of astigmatism -- which would result in a different sensitivity / noise performance between pitch and yaw, means that pitch is only ~2.1% worse than yaw.      

Great! We're good to go!