Early tests both in the lab and on sky revealed a lower than expected instrument visibility from JouFLU. These low visibilities raised concern that the combiner may be exhibiting either differential polarization rotation, differential polarization delay, or a combination of both.
0 60 120 180 240 300 360 420 480 540 600 0 0.05 0.1 0.15 0.2 0.25 0.3 0 60 120 180 240 300 360 420 480 540 600 Beam A Beam B 0.25-0.3 0.2-0.25 0.15-0.2 0.1-0.15 0.05-0.1 0-0.05 Visibility Amplitude
Figure 4.33: The effects of adjustment of the fiber polarization for each of the two beams on white light fringe visibility. Each fiber has a knob which affects the bend of the fiber. Each knob was incrementally adjusted in steps of 60 (arbitrary units) to give 100 data points over the full range of travel. Based on these results MONA was set to the maximum V (480 and 180 for the top and bottom knobs, respectively).
As part of theJouFLUproject, the fiber combiner box MONA was sent toLVFfor
re-calibration and adjustment. The fiber heads were cleaned and two knobs with numbered scales were added to provide precise adjustment of the polarization rotation (“Mickey ears”) of the fibers. Once installed back at theCHARAArray, the interferometric signal throughput was maximized. This was achieved by scanning through the range of the polarization
adjustment for each beam while measuring the visibility of lab fringes generated by a
controlledWL(seeFigure 4.33). However, even after this optimization process, the observed visibilities were lower than expected.
To determine the cause of the low visibility, a battery of tests was conducted using two linear K-band polarizers on rotating mounts. Table 4.7describes the various test conditions.
Universally for all tests the following guidelines were followed: one data file was recorded for each move of rotated polarizer; one polarizer was always held stationary at either 0◦ or 90◦; and the other polarizer was rotated in steps of 10◦ from 0◦ to 180◦.
Table 4.7: *should have fringes, others are tests of photometry. Test 0 is to check the po- larizers with respect to each other to determine their polarization axis. Polarizers were either placed at theCHARA WLsource, the beam inputs at the edge of theJouFLUoptical table, or at theOUTPUTstage immediately before the camera aperture.
Name Polarizer 1 Polarizer 1 Polarizer 2 Polarizer 2 Comments
position rotation (◦) position rotation (◦)
baseline — — — — no polarizers
Test 0-b b input 0 b input rotated beam a blocked
Test 0-a a input 0 a input rotated beam b blocked
Test 1b-0 output 0 b input rotated beam a blocked
Test 1a-0 output 0 a input rotated beam b blocked
Test 1b-90 output 90 b input rotated beam a blocked
Test 1a-90 output 90 a input rotated beam b blocked
*Test 2b-0 b input rotated a input 0
*Test 2a-0 a input rotated b input 0
*Test 2b-90 b input rotated a input 90
*Test 2a-90 a input rotated b input 90
*Test 3-0 WL rotated output 0
*Test 3-90 WL rotated output 90
For Test 1, a single polarizer was placed in either beam A or beam B, and the other beam was blocked; another polarizer was placed at the combiner output, before the detector. The photometry of each beam was recorded as the input polarizer was rotated (SeeFigure 4.34). As expected with two linear polarizers in-line with each other, the photon flux at the output
varies sinusoidally with the angle of rotation of the polarizer. However, this sinusoidal pattern does not match between the two beams and a difference in phase is apparent. This is
indicative of the combiner displaying uncorrected differential polarization rotation. By tracking the shift in phase, the amount of differential polarization rotation can be determined (See Table 4.8).
The amount of differential polarization rotation can be found by looking atFigure 4.34and tracing the polarization angle where the signal peak lies,
For0◦output polarization:
A10−B10 =100◦−40◦ = 50◦
A20−B20 =180◦−100◦ = 80◦
(4.8)
For90◦ output polarization:
A190−B190=160◦−125◦ = 35◦
A290−B290=100◦−170◦ =−70◦ = 110◦
(4.9)
So for the difference between the two beams in each polarization:
(A20−B20)−(A10 −B10) =80◦−50◦ = 30◦
(A290−B290)−(A190−B190) =110◦−35◦ = 75◦
(4.10)
Table 4.8: Differential polarization rotation.
Name Signal 1 Signal 2 Difference
(◦) (◦) (◦)
Test1-0 50 80 30
-5 0 5 10 15 20 25 30 35 40 45 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 1b-0 1a-0 1b-90 1a-90 Coun ts
Rotation of Polarizer (deg)
Photometry
SHUTTER_A Sig1 SHUTTER_A Sig2 SHUTTER_B Sig1 SHUTTER_B Sig2
|--A-- --O--P0 Pr--B-- Pr--A-- --O--P0 |--B-- |--A-- --O--P90 Pr--B-- Pr--A-- --O--P90 |--B--
A - beam A B - beam B O - output | - beam blocked Pr - Polarizer is rotated P0 - Polarizer set to 0 deg and held P90 - Polarizer set to 90 deg and held 1.2
CLASSIC V_LOGNORM
Detector1 Mean Detector2 Mean Combined Mean
B2 A2 B1 A1 B2 B1 A1 A2
Figure 4.34: Photometry of the JouFLUinterferometric signal channels for tests 1b-0, 1a-0, 1b-90, 1a-90. As expected when two polarizers are placed in front of each other and one is rotated, there is a sinusoidal variation in the amount of flux transmitted. The evidence for differential polarization rotation comes from the difference in phase of these variations. The left two plots are for the 0◦ output polarization, while the right two plots are for the 90◦ output polarization.
Test 2 consisted of placing one polarizer at the input of each beam and rotating one of the polarizers, while holding the other stationary. This was performed on both the CLASSIC CHARAbeam combiner and theJouFLUcombiner. The results are shown inFigure 4.35and Figure 4.36, respectively. Here it is apparent that there are complex polarization effects affectingJouFLUand resulting in a disturbance to the expected fringe contrast.
The final experiment, Test 3, placed one polarizer atWLsource and one at the combiner output in front of the detector. This polarizer was then rotated. Figure 4.39andFigure 4.40 compare the results of this test on bothJouFLUand CLASSIC.
The results of these tests, in particularFigure 4.40, match the model condition given by Equation 4.19below where dφ = 109◦ with a 90◦ periodicity (Figure 4.41). This periodicity
A - beam A B - beam B O - output | - beam blocked Pr - Polarizer is rotated P0 - Polarizer set to 0 deg and held P90 - Polarizer set to 90 deg and held 0 0.2 0.4 0.6 0.8 1 1.2 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 2b-0 2a-0 2b-90 2a-90 V
Rotation of Polarizer (deg)
CLASSIC V_LOGNORM
Detector1 Mean Detector2 Mean Combined Mean
P0--A-- --O-- Pr--B-- Pr--A-- --O-- P0--B-- P90--A-- --O-- Pr--B-- Pr--A-- --O-- P90--B--
A - beam A B - beam B O - output | - beam blocked Pr - Polarizer is rotated P0 - Polarizer set to 0 deg and held P90 - Polarizer set to 90 deg and held
Figure 4.35: Visibility measurements with CLASSIC for tests 2b-0, 2a-0, 2b-90, and 2a-90. These visibility plots are as expected for the case of superposition of two linearly polarized beams. 0 0.2 0.4 0.6 0.8 1 1.2 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 2b-0 2a-0 2b-90 2a-90 V
Rotation of Polarizer (deg)
JouFLU V_LOGNORM
Detector1 Mean Detector2 Mean Combined Mean
P0--A-- --O-- Pr--B-- Pr--A-- --O-- P0--B-- P90--A-- --O-- Pr--B-- Pr--A-- --O-- P90--B--
A - beam A B - beam B O - output | - beam blocked Pr - Polarizer is rotated P0 - Polarizer set to 0 deg and held P90 - Polarizer set to 90 deg and held
Figure 4.36: Visibility measurements with JouFLU for tests 2b-0, 2a-0, 2b-90, and 2a-90. In this case it is apparent that there are more complex polarization effects present than the expected superposition of two linearly polarized beams.
suggests differential phase delay is occurring inside the beam combiner. Differential phase delay, along with polarization rotation, finite fringe and temporal sampling, bandwidth smearing, and beam imbalance, results in a maximum visibility ofVmax ≈0.73.
Figure 4.37: CLASSIC test 3 photometry shows no significant variation in flux.
Figure 4.38: JouFLU test 3 photometry shows no significant variation in flux compared to CLASSIC. This rules out variation in flux as a cause of the modulation of visibility seen during test 3.
This is our case, test 3, of having one polarizer at the WL source and one at the camera. So we have a two linearly polarized beams entering MONA, there they are superimposed and gain some polarization state, then pass through the output polarizer and are again linearly polarized. We essentially have the case of circularly polarized light, superimposed and then passing through a linear polarizer.
Figure 4.39: CLASSIC test 3 shows no evidence of differential polarization phase delay.
Figure 4.40: JouFLUtest 3 shows strong evidence of differential polarization phase delay.
If we assume the source is circularly polarized and we measure two orthogonal polarizations in thexandyplanes and start with the two input beams:
E1 = cosθxˆ+ sinθyˆ
E2 = cosθeiφxˆ+ sinθei(φ+∆φ)y.ˆ
(4.11)
whereφis the differential phase of polarizationxbetween the two beams,φ+ ∆φis the differential phase for polarizationy,∆φ is the maximum phase delay between the two polarizations, andθ is the angle of a linear polarizer inserted into the beam.
The superposition of the polarized waves gives the total intensity, I, as
I =|E1+E2|2. (4.12)
SubstitutingEquation 4.11intoEquation 4.12gives:
I =
(cosθ1 +eiφxˆ+ (sinθ1 +ei(φ+∆φ)yˆ
2 = cos2θ 1 +e iφ 2 + sin2θ e i(φ+∆φ) 2 = cos2θ 1 +eiφ 1 +e−iφ + sin2θ 1 +ei(φ+∆φ) 1 +e−i(φ+∆φ) . (4.13)
From the relationship between sine, cosine, and exponential forms:e±φ = cosφ±isinφ, this
becomes,
I = cos2θ 2 + cosφ−isin (φ) + cosφ+isinφ+
sin2θ 2 + cos (φ+ ∆φ)−isin (φ+ ∆φ) + cos (φ+ ∆φ) +isin (φ+ ∆φ).
(4.14)
The imaginary terms cancel, leaving,
I = cos2θ(2 + 2 cosφ) + sin2θ(2 + 2 cos (φ+ ∆φ)). (4.15)
This can be further simplified and making use of the identity: cos2φ+ sin2φ = 1, takes the form
I = 2
1 + cos2θcosφ+ sin2θcos (φ+ ∆φ)
. (4.16)
Using the identity,cos (φ+ ∆φ) = cosφcos (∆φ)−sinφsin (∆φ), this can be written as,
I =21 + cos2θcosφ+ sin2θ(cosφcos (∆φ)−sinφsin (∆φ)) =2 [1 +acosφ−bsinφ].
wherea= cos2θ+ cos (∆φ) sin2θandb = sin (∆φ) sin2θ. Now we have I in terms of the phase,φ, and it can be expressed as,
I =2 1 +√a2+b2 a √ a2+b2cosφ− b √ a2+b2 sinφ ! . (4.18)
Knowing we wantI of the formI = 2(1 +V cos (φ+φ0))means that we can state
V =√a2+b2 and differential delay with respect to polarization gives
I = 21 + cosφcos2θ+ cos (φ+ ∆φ) sin2θ. (4.19)
This is modeled inFigure 4.41and matches the empirical results shown inFigure 4.40. We find that there is a differential delay in phase between orthogonal polarizations equal to109◦.
0 50 100 150 200 polarizer angle 0.0 0.2 0.4 0.6 0.8 Visibility
Figure 4.41: Results of model to determine the amount of polarization phase delay.
As a result of these series of tests, we have found evidence of differential polarization rotation and differential phase delay. Differential polarization rotation is analogous to the visibility loss
resulting from beam intensity mismatch with the following effects: Vobs =V 2 cos (α) 1 + cos2(α), (4.20) where for 50◦ →Vmax ≈90% and 70◦ →Vmax ≈60%.
Additionally, we noticed that CHARA laboratory white-light source (WL) is probably not circularly polarized. We observe an averageV ≈0.42instead of the expected 0.59. So, we may conclude that theWLis elliptically polarized (close to 50◦or 150◦).
External polarization rotation controllers that were used on a previous beam combiner have been sent toCHARAand, if necessary, can be added to theJouFLUoptical bench. This would provide an extended range of polarization rotation control when used with the full range of the Mickey ears. It remains to be seen if the gain from matching polarization rotation would compensate for the sensitivity that would be lost by this method.
To correct the polarization phase delay, lithium niobate plates are planned for incorporation in the beams prior to reaching theJouFLUoptical table. These plates would beARcoated for K band and mounted on rotation stages with the faces perpendicular to the beam axis.
Differential rotation of the plates would induce a delay in the polarization phase of that beam by increasing the path for that beam polarization. A similar method to control polarization
phase delay was introduced toPIONIER, a 4-beam H band beam combiner at theVLTI (Lazareff et al. 2012). This technique enabled them to reach instrumental contrasts of
≈98.5% with a throughput loss of only≈10%.