D ESIGN P HILOSOPHY
The Thermal Compensation System (TCS) effectively addresses a variety of thermal effects in interferometers caused by different optics While efforts to minimize coating and substrate absorptions are ongoing, TCS offers significant flexibility for correcting optics that may not meet specifications Additionally, TCS includes an online tool for rectifying mirror radius errors and helps mitigate acoustic parametric instabilities by managing the transverse mode spectrum of the arm cavities Although TCS can correct for inhomogeneities in optical absorption, the specific size or distribution of these inhomogeneities cannot be predetermined.
TCS will prioritize flexibility in its design, addressing the need for precise measurement of thermal aberrations in individual optics This necessity was highlighted by the shortcomings observed in initial LIGO, prompting TCS to incorporate sensors on both the core optics and the main interferometer beam for enhanced performance.
The design philosophy of TCS emphasizes the use of fused silica for the test mass substrates in Advanced LIGO, ensuring optimal performance Additionally, it is based on the assumption that the mirror radii of curvature are specifically optimized for cold operational conditions.
O VERALL L AYOUT OF TCS
[Includes revisions to the conceptual design developed since the CDR, noted in boldface.]
The positions of the thermal compensators and optical sensors are indicated schematically in Figure
1 The phase cameras monitoring pickoff ports of the main interferometer beam are not shown.
The main thermal compensation for homogeneous absorption in optics will utilize carbon dioxide laser projectors, replacing the shielded ring heaters from the previous version Calculations indicate that the noise and power requirements for the CO2 laser projectors are feasible with current technology Compensation and control of the TM HR surfaces will be achieved using shielded ring heaters within the quad SUS structure, with four heaters for each interferometer, positioned around each test mass These test mass ring heaters will regulate the arm cavity mode shape and provide limited compensation for thermorefractive aberrations in the recycling cavities Additionally, they may be employed to temperature-tune and mitigate radiation-pressure parametric instabilities.
In his thesis, Ryan Lawrence highlighted two key benefits of implementing thermal compensation on a compensation plate instead of directly on the input test mass Firstly, effective compensation necessitates achieving zero net heat flow on the barrel of the compensated optic This approach significantly enhances performance and efficiency.
2 RODA : CP to be the Ultimate Mass in the ITM Reaction Chain, LIGO document LIGO-M040005-01-Y.
3 TCS Actuator Noise Coupling, LIGO document LIGO-T060224-00-D.
Heat flow from the barrel creates a radial thermal gradient, leading to a thermorefractive optical phase gradient Insulating the test mass barrel with a low-emissivity coating or shield is essential due to the thermal interaction between the input test mass (ITM) and the compensation plate (CP) Additionally, since the CP is located entirely within the recycling cavity and lacks high-reflective (HR) surfaces, its susceptibility to compensator noise is significantly reduced compared to a test mass However, a notable limitation of the compensation plate is its inability to correct errors within the arm cavities.
Carbon dioxide laser projectors can provide compensation of non-axisymmetric thermal lensing. These projectors will be located outside the vacuum envelope for easy modification of the projected thermal profile
Each optic subjected to significant thermal load will undergo independent monitoring, focusing on the HR face of each test mass for deformation The phase profile of the input test mass and compensation plate will be assessed through reflection on-axis from the recycling cavity side, utilizing a probe beam that enters via a pickoff port, such as the wedged AR face of the beamsplitter Although no compensation is planned for the beamsplitter itself, it contributes approximately 10% to the thermal aberration within the interferometer and will be monitored in transmission However, if a special low-absorption glass is utilized for the beamsplitter, the need for this monitoring may be eliminated due to negligible thermal lens effects.
Understanding the mode profile of the interferometer beam is crucial, even though knowledge of each optic's phase profile is important This mode profile will be monitored at the pickoff ports of the interferometer using phase cameras.
5 Heating of the ITM by the Compensation Plate in Advanced LIGO, LIGO document LIGO-T070123-00-D.
Figure 1: layout of thermal compensators and thermal compensation sensors Red dots: shielded ring heaters Blue arrows: optical path sensors (Hartmann sensors) Green projections: carbon dioxide laser heaters.
Thermal aberrations in interferometers will be detected using various complementary techniques Initially, the degree of aberration can be observed through IFO channels like SPOB and AS_I, which represent scalar quantities related to the light conversion from the fundamental cavity mode To analyze the spatial structure of the cavity mode, phase cameras and Spiricons will sample the interferometer beam at multiple ports However, the active control of thermal aberrations using spatial sensors remains unproven, and the coupled cavity nature of the interferometer complicates the extraction of individual mirror aberrations Consequently, wavefront sensors will be employed to individually assess the input test masses and beamsplitter Ultimately, the thermal control system is expected to incorporate a combination of these sensors as inputs.
Figure 2 shows this control scheme for the TCS system in a block diagram.
Figure 2: Block diagram of the TCS system.
A CTUATORS
Test Mass Ring Heater
The self-heating of test masses primarily occurs through absorption in the HR coatings, leading to a deformation that creates a bump at the center of the test mass faces, resulting in a non-spherical surface profile This alteration causes the cavity to become less concentric and reduces the spot sizes at the mirrors However, with a uniform absorption level of 0.5 ppm anticipated in Advanced LIGO, this deviation from sphericity does not significantly affect the Gaussian nature of the arm cavity resonant modes Figures illustrate the surface deformation due to 0.5 ppm absorption and the corresponding arm cavity mode, which fits a Gaussian profile with a spot size of 5.4 cm.
The figure illustrates the surface deformation of the TM due to self-heating from the interferometer, along with the corresponding intensity profile of the arm cavity mode In the arm cavity mode representation, the simulation is depicted in green, while the optimal Gaussian fit is shown in red.
Assuming an absorption rate of 0.5 ppm per coating for each test mass, the ITM spot size ranges from 6 cm at low power to 5.4 cm at full power While we might accept this variation, it results in an approximate 15% increase in thermal noise levels To preserve the arm cavity mode structure, it is essential to control the radii of curvature of all test masses.
Figure 4: Arm cavity mode intensity profile resulting from the deformation in Figure 3 The simulation is in green, and the best fit gaussian in red.
A conceptual design of the test mass ring heater is shown in Figure 5
The suspended test mass features a shielded ring heater strategically positioned within a parabolic shield, rendering it invisible, along with the mounting system that secures both the ring and shield to the suspension cage.
The ring heater features a diameter of 360 mm and a thickness of 5 mm, surrounded by a 20 mm wide parabolic shield that positions the ring at its focus, maintaining a 4 mm gap from the test mass barrel Designed with axisymmetry in mind, modifications to the ring or shield near the optic flats have not been addressed It will be strategically mounted near the AR face of the optic, with its exact positioning and installation methods to be finalized in collaboration with SUS.
Figure 6: ring compensated test mass thermoelastic HR surface deformation.
The thermal deformation of the HR surface of the test mass near the AR face is largely unaffected by the heat distribution, resulting in a spherical concavity The total thermoelastic deformation for optimized compensation indicates a nearly flat profile, yielding an intensity pattern closely resembling the fundamental Gaussian with a 6 cm spot size at the ITM Although the compensated mode exhibits slightly more power at larger radii than the Gaussian, it incurs a round-trip diffraction loss of 22 ppm compared to less than 1 ppm for the Gaussian, with an overlap of 99.977% Achieving this compensation requires 11W of incident heat on the optic, and due to the effective coverage of the reflective shield, most of the radiated ring power is expected to impact the optic The radiated power is approximately 0.1 W/cm, significantly lower than the 2.5 W/cm threshold where the blackbody spectrum from a ring heater enters the transmissive band of fused silica.
6 Lawrence’s thesis, p 215. should provide up to 22W to the optic if needed This conceptual design satisfies the requirement in Section 3.1.2.1 of the TCS DRD.
Applying heat directly to the test mass alters the thermorefractive phase profile, impacting thermal aberration in the recycling cavity Thermal phase maps for reflection from the ITM's AR side illustrate the effects of thermal compensation via a test mass ring heater While compensation is possible with a CO2 laser projector, it requires optimal intensity stability Therefore, the preferred approach is to maintain a 6 cm spot size at the ITM by adjusting the ETM's ring heater This strategy is detailed in LIGO document T060214-01-D, with noise coupling analysis in document T060224-00-D indicating that CO2 laser projector intensity noise is marginally sufficient.
Figure 7: Arm cavity mode intensity profile resulting from surface deformation in Figure 6.
As before, the FFT simulation is in green, and the best-fit Gaussian (with 6 cm spot size at ITM) in red.
This design minimizes sensitivity to actuator noise fluctuations by positioning the heating mechanism on the barrel, away from the IFO beam, allowing for more stable performance Additionally, the radiation pressure effects average out to zero across the mass, although there is a minor coupling of overall power fluctuations.
HR surface displacement occurs due to power fluctuations that lead to variations in the mirror's flexure, resulting in changes in the HR surface position relative to the mirror’s center of mass This phenomenon of noise coupling is further explored in Section 8.1.
Figure 8: Phase profiles through directly heated ITM, without (left) and with (right) test mass ring heater compensation.
Compensation Plate
The compensation plate will utilize thermal actuation from an external CO2 laser projector to address thermal aberration in recycling cavities This projector features a reconfigurable heating pattern, enabling quick characterization and enhancements While earlier research suggested the use of shielded ring heaters for quieter power delivery, the noise couplings on the compensation plate support the use of a stabilized CO2 laser Additionally, the challenges of integrating the ring heater with the suspension structure, including mechanical and optical interferences, have rendered its design uncertain.
The High Power Test Facility at Gingin has demonstrated the effectiveness of using a compensation plate to correct thermal aberrations While a detailed analysis of the compensation quality is currently lacking, Ryan Lawrence's modeling indicates that employing a ring heater on a compensation plate can reduce thermal aberration to 10^-4.1 of its uncorrected value, particularly in cases of homogeneous absorption, as assessed by the scatter of power from the TEM00 mode Advanced LIGO estimates suggest that a correction of approximately 10^-3 will be necessary at maximum power levels, making the use of a compensation plate a practical solution.
The compensation plate (CP) directly interacts with the interferometer (IFO) beam and must meet stringent criteria similar to core optics, including displacement noise, absorption, scatter, and index homogeneity, along with effective antireflection coatings Additionally, the CP can generate pickoff beams for IFO sensing and control Applying antireflection coatings, wedges, or compensating polishes to the CP poses no challenges Its isolation requirements are significantly less stringent than those for the input test masses (ITMs), allowing for effective suspension from the ITM reaction chain The CP will be suspended using two wire loops and will feature no polished flats on its sides, with dimensions of 170 mm in radius and 130 mm in thickness, an increase from the previous 65 mm, and constructed from low-absorbing Suprasil 311.
At 2 ppm/cm, the CP absorbs only 36 mW of power, significantly lower than the 0.5 W absorbed by the ITM Consequently, the additional aberration introduced by the CP is minimal and can be effectively corrected alongside the aberration from the ITM.
Enhancing compensation for optical performance can be achieved by insulating the barrel, such as using a reflective shield or a low emissivity coating While this approach was not included in the current design, it remains a viable option for improvement.
Thermal lensing significantly impacts RF sideband efficiency, arm cavity power gain, and, most critically, GW sideband extraction efficiency The quality of thermal compensation is most stringently dictated by the GW sideband extraction efficiency, which requires the TEM00 mode to overlap with itself with an accuracy of better than 99.9% This precision is essential to ensure that the GW sideband output amplitude remains within 5% of its nominal value.
Figure 9: Radial phase profile of an uncompensated ITM at full IFO power.
7 See RODA: Compensation Plate dimensions, LIGO document LIGO-M060305-01-Y.
The phase profile of the ITM in the recycling cavity, illustrated in Figure 9, is compared with the optimized profile from a ring heater (Figure 10) and the compensated phase profile (Figure 11) With a baseline ITM absorption of 8 and a total TCS power of 6 W incident on the CP, the mode overlap for the TEM00 mode through the compensated optical phase profile reaches an impressive 99.99% This value satisfies the criteria outlined in Sections 3.1.2.2, 3.1.2.3, and 3.1.2.5 of the Advanced LIGO TCS Design Requirements Document In contrast, the uncompensated mode overlap is significantly lower at only 49%.
We expect a CO2 laser projector to be easily able to generate this heating profile.
Figure 10: Compensation heating profile from optimized shielded ring heater.TCS must also minimize the stray light at the dark port, in concert with the output mode cleaner
This is discussed in more detail in Section 7.2
8 850 kW arm power and 2100 W through the substrate, 5 ppm coating absorption and 2 ppm/cm substrate absorption.
Figure 11: ITM phase profile after compensation by the heating pattern in Figure 11.
CO 2 Laser Projector
The CO2 laser projector operates outside a vacuum, allowing for easy adjustments to enhance its heating pattern Our primary design features a fixed-mask staring projector, while we also introduce a scanned projector concept that can be developed for continuous adjustment of the heating pattern as needed.
The design closely resembles the CO2 laser projector used in initial LIGO, differing mainly in beam projection onto the compensator plate, the use of a 25W laser, and simultaneous intensity modulation via an AOM and rotating polarizers The more powerful laser ensures adequate headroom while preventing excessive deflection efficiency in the AOM, which can cause beam wander The proposed layout, illustrated in Figure 12, includes a mask design for full compensation like in initial LIGO, but can also be customized to address manufacturing tolerances and small inhomogeneities The specific mask illumination pattern will be developed using data from Hartmann sensors and core optic metrology prior to installation Additionally, optics with conical surfaces, known as 'axicons,' may be utilized to efficiently transform the Gaussian beam into an annulus for further adjustment with the mask.
Figure 12: Fixed-mask staring CO2 projector
The design enables control over the overall compensation intensity, making it user-friendly but slow to adapt, as creating new masks could take at least a week The frequency of new mask requirements remains uncertain Options for the mask include the machined disks from the initial LIGO setup or ZnSe flats with reflective coatings, offering enhanced flexibility in compensation patterns.
The Boston Electronics PVM-10.6 PD detector will be utilized, featuring a noise floor of approximately 10^-9 V/√Hz and a saturation level around 10 mV, making power stabilization at about 10^-7/√Hz achievable.
The CO2 laser projector requires precise power adjustments due to variations in the optic absorption pattern, making exact power predictions challenging With a nominal power absorption of 6 W from an optimized ring heater, the CO2 laser must output at least 25 W, considering the mask's 24% efficiency in converting the Gaussian beam to the desired heating pattern Additionally, to compensate for a 1 mm² spot that absorbs an excess of 1 ppm (approximately 0.14 mW), the laser must distribute this excess heat across the optic, necessitating a total power of 9 W Consequently, a 25 W laser is deemed sufficient for optimal performance.
Ryan Lawrence's innovative CO2 laser projector design utilized an intensity-modulated beam that scanned in a spiral raster pattern with galvanometer mirror deflectors Although this method offered thermal compensation for point heat sources, his noise analysis failed to adequately account for the significant upconversion noise within the LIGO bandwidth For a detailed examination, refer to Section 8.2.
A viable approach for a scanned laser system involves utilizing acousto-optic modulators to scan the laser across the optic face at significantly higher frequencies instead of traditional galvanometers This method offers two key benefits: it ensures that the scanning frequency and its harmonics exceed the LIGO bandwidth, and it reduces injected noise, which scales linearly with pixel dwell time and inversely with scan frequency.
The limitation occurs when the injected phase noise is strong enough to push the optical system beyond its linear operating range For instance, optical path variations at the 60 pm level equate to 350 microradians at a wavelength of 1.064 microns The linear range of a cavity locking scheme is approximately 2√F, with F representing the cavity finesse In the case of Advanced LIGO, the arm finesse is around 730, resulting in a linear range of about 8600 microradians.
The CO2 laser projector's intensity within the LIGO bandwidth needs to maintain stability at a relative intensity noise (RIN) level of approximately 10^-7/√Hz, posing a significant challenge for systems operating at high modulation frequencies.
The conceptual layout of the CO2 laser projector optical beams is illustrated in Figure 13, depicting an unfolded interferometer The CO2 laser beam starts at the TCS table and enters the vacuum through a viewport in the ITM BSC chamber It is then directed by a steering mirror to another mirror positioned lower in the BS BSC chamber, where it reflects back to the CP at an angle of approximately 7 degrees from normal incidence Although the CO2 laser beam may exhibit slight divergence upon entering the vacuum, similar to the initial LIGO setup, the final steering mirror can incorporate magnifying power to maintain the compactness of the in-vacuum optics.
Figure 13: In-vacuum optics of the CO2 laser projectors.
Folded IFO TCS Actuator Design
The folded interferometer lacks a long optical path from the beam splitter to the cavity, requiring the beam to expand more rapidly and strike at a significant angle This design is promising but needs to be developed alongside the ITM/FM suspension assembly for optimal performance.
Simultaneous Compensation on the ITM and CP
The simultaneous presence of thermal distortions in both the recycling and arm cavities poses a challenge for TCS design When compensating the test masses to maintain a 6 cm arm cavity spot size, the resulting thermal phase profile of the ITM deviates from the intended design of the shielded ring heater Conversely, without direct compensation, the arm cavity mode spot size decreases to 5.4 cm, rendering the shielded ring heater ineffective once again Given that the CO2 laser projector will effectively manage all heating patterns, except potentially for compensating the ITM ring heater's thermal lens, the design approach will focus on eliminating the shielded ring heater, minimizing the ITM ring heater's use, and fully relying on the CO2 laser projector for heating applications.
Beamsplitter Compensation
The beamsplitter does not require direct compensation as it only contributes approximately 10% of the thermal lens effect in the recycling cavities, which can be largely addressed by the compensation plates However, since the beamsplitter impacts the thermal lens differently in the power and signal recycling cavities, it is not possible to correct its entire effect simultaneously at the compensation plates While this may not pose a significant issue, the option to retrofit thermal compensation onto the beamsplitter remains in the AdLIGO optical layout.
TCS S ENSORS
Dedicated Sensors
[Modified to reflect adoption of Hartmann sensors over WLISMI sensors]
The dedicated sensors include a wavefront sensing device and a probe beam that captures thermal aberration information According to the TCS Design Requirements Document in section 3.1.2.6, the wavefront sensor must examine the central area of the ITM and CP, covering a radius of at least 112 mm.
In this section we present a conceptual layout of the in-vacuum optics for the dedicated sensor probe beams, and describe the tradeoffs that motivate the conceptual design.
The most critical thermal aberrations occur in the ITM/CP pairs, making their dedicated sensors essential Achieving collinear probing with the main interferometer beam eliminates parallax between the ITM and CP, resulting in an optimally compensated thermal phase profile.
The document LIGO-T060215-01-D discusses nine test mass thermal compensation strategies, highlighting that the phase measurement can be relative rather than absolute, as any errors in measuring the cold optic are replicated in the hot optic and can be offset While the beamsplitter ideally should not contribute to thermal aberration, it is acknowledged that this is not the case However, the thermal lensing effect of the beamsplitter is expected to be only about 5% of that of the ITM thermal lens, resulting in a minimally altered compensated profile It is also noted that an off-axis sensor would encounter similar beamsplitter issues.
On-axis sensors require beam paths into the main IFO beam We have two alternative designs which could satisfy requirements.
The wedged anti-reflective (AR) face of the beamsplitter plays a crucial role in coupling TCS ITM/CP sensor probe beams into the main beam, as illustrated in Figure 14 Although the diagram depicts a horizontal wedge for clarity, the actual beamsplitter features a vertical wedge, which maintains the design's integrity This wedge effectively decouples the two ITMs from the perspective of the sensor probe beams For instance, a sensor probe beam striking the beamsplitter's AR surface near the signal mirror reflects collinearly with the main IFO beam directed toward ITMx In contrast, the probe beam that passes through the beamsplitter descends towards ITMy at a slower rate due to the wedge, ultimately missing ITMy altogether Thus, to a first approximation, this probe beam does not interact with ITMy.
The probe beam for ITMy presents challenges as it must be coaxial with the main beam in the beamsplitter substrate before reaching the ITMy This probe beam, incident from below near the PRM and coupled by reflection off the beamsplitter's anti-reflective face, encounters reflection from the high-reflective face of the beamsplitter, which then probes ITMx.
This problem can be avoided if the sensor probe wavelength is fully transmitted by the BS HR face.
The BS HR coating is engineered to ensure that the BS HR face achieves a transmittance greater than 99% This design effectively attenuates light coupled to the incorrect Input Test Mirror (ITM) by over 10,000 times upon its return to the dedicated sensor, significantly enhancing the detection of the desired beam.
Higher-order beams circulate multiple times within the recycling cavities before exiting through the BS AR face Due to the increased number of reflections from partially reflecting optics, these higher-order paths experience significant attenuation.
The BS AR surface can be engineered to reflect the probe beam almost perfectly, with the probe beam positioned at a slight angle to the ITM/CP axis This slight angle results in a deflection of the return beam from the incident beam, allowing for the separation and disposal of higher-order probe beam paths, which are longer and thus experience greater deflection Models indicate that a tilt of 0.05√ is sufficient for this purpose, introducing a minimal parallax of only 260 microns.
One of the TCS dedicated sensor beams can share the POB telescope if it is installed on one of the correct ports of the beamsplitter.
The TCS sensor probe beams can be effectively injected through the rear face of a mirror in each mode-matching telescope, given the high transmission condition of the BS HR face This alternative injection scheme offers additional possibilities for optimizing the sensor's performance.
Passing TCS sensor beams through recycling mirrors twice can reduce power, but allows for smaller, cost-effective, and lighter sensor beam telescopes In a stable recycling cavity design with mode matching telescopes, power loss at recycling mirrors is manageable However, input optics may experience significant variations in laser power during interferometer activation, leading to thermal lensing issues that need to be addressed Conversely, the output mode-matching telescope does not face this challenge.
At present, there is no quantitative requirement on the HR and AR reflectivities of the core optics at the probe wavelengths.
The configuration of dedicated sensor probe insertion points at the beamsplitter is illustrated in Figure 14 In this diagram, the solid lines represent the trajectories of the primary interferometer (IFO) beam, while the dotted lines indicate the paths of the injected probe beams, except where they coincide with the main IFO beam.
The optical layout for the ITMx sensor, depicted in Figure 15, includes steering mirrors and beam-expanding telescopes To mitigate stray light issues, the telescopes must be designed as reflectors instead of the refractors illustrated, although this reflective design will closely resemble the Pickoff Telescope configuration.
The ITM sensor probe beams will sample the thermal aberrations of the beamsplitter in this configuration, and the impact on the wavefront sensor varies based on the sensor type, as detailed in Section 4.2.1.2.
To ensure effective Stray Light Control, it is essential to remove residual power from the main IFO beam at the pickoff port using a hot or cold mirror Additionally, the TCS probe beam must be separated from the pickoff and ASP signals through the use of dichroic mirrors This process is crucial for maintaining optimal performance from ITMx to ITMy, SRM, and PRM.
The layout of the steering mirror and telescope for the ITM CP sensors involves a probe beam that enters the vacuum from the lower right It is elevated by a periscope within the vacuum, then expanded by a telescope positioned above the SRM as it moves leftward Finally, the beam is directed downward by another periscope, just below the optical table, for injection into the BS AR face.
Phase Camera Design
The phase cameras in Advanced LIGO are similar to those in initial LIGO, with the main distinction being the use of larger RF modulation frequencies, reaching up to 180 MHz However, since the photoreceiver has a bandwidth of 1 GHz, this difference is negligible in practical terms.
The phase camera currently has two main drawbacks: the vibrations caused by the galvanometer mirror can disrupt nearby equipment, and the scan rate is limited to one every half second These issues can be resolved by using a crossed pair of acousto-optic modulators (AOM) instead of a galvanometer, which would allow for scans of 4000 pixels in less than a millisecond Additionally, regardless of the scanning technique used, the pickoff beam will be mixed with a sample of the main laser beam, offset by an AOM to create a distinct beat frequency This sample can be transmitted to the phase camera via optical fiber and expanded to achieve a nearly flat field, thereby simplifying the analysis of the resulting images.
An alternative to the scanned image phase camera concept has been proposed by Rana Adhikari.
He notes that 1064nm-sensitive CCD cameras with bandwidth in the MHz range are on the verge of commercial availability
Phase cameras can be strategically installed at various pickoff ports of the main beam, with POB, POY, and ASP being the most informative regarding thermal aberrations We recommend replacing the bullseye sensor currently utilized in LIGO for TCS common mode control with the phase camera, as it measures the same parameters effectively.
13 “Optical Layout for Advanced LIGO,” Dennis Coyne, LIGO-T010076-01-D, section 2.
5 Notes on Sensor and Actuator Beam Distortion
A key design consideration for beam expanding telescopes utilized by TCS dedicated sensors is the potential distortion of the large probe beam To mitigate this distortion, it is essential to either employ very large and costly optics or utilize multiple element telescopes.
A certain level of distortion, such as barrel distortion, can be tolerated in TCS sensors without affecting their functionality This distortion causes a Cartesian grid of pixels on the CCD plane to appear non-Cartesian at the optic face, with points further from the optic axis being more deflected Although the CCD camera captures a distorted image of the optic's phase profile, this distortion is predictable and can be measured prior to vacuum installation Consequently, it can be accounted for during data processing of the thermal phase profile, ensuring that the operation of the TCS sensor remains unaffected.
The CO2 laser projector optics require the laser beam to strike the CP off-axis, resulting in a foreshortened heat pattern This distortion can be effectively managed by adjusting the mask used to create the heater pattern, allowing for precise control over the projected output.
High-quality, non-distorting optics are preferred for the TCS sensor and actuator beams; however, they are not mandatory Currently, there are no specific quantitative standards regarding distortion in the optical train of the TCS sensor and actuator.
Thermal aberrations in fused silica optics primarily arise from thermorefractive effects, with thermal expansion effects playing a minor role due to the thermal expansion coefficient being only 6% of the thermorefractive coefficient Although fused silica possesses a stress-optical coefficient that can contribute to thermal aberrations, its impact is minimal, accounting for only 1% of the thermorefractive effect Nevertheless, the stress-optical effect creates a unique phenomenon, as the stress fields within the optic induce local birefringence This results in light passing through the optic being rotated into an orthogonal polarization, with the degree of rotation varying across the mode profile.
Efim Khazanov's group at the IAP has determined that the light loss due to orthogonal polarization in the uncompensated ITM is 4.5 ppm, which is significantly lower than the pickoff reflectivity and can be disregarded Although the thermal depolarization in a compensated ITM/CP pair has not been quantified, it is expected to be of a similar magnitude.
The depolarization could potentially be magnified if it coherently builds in the recycling cavity beam over multiple round trips This effect has not yet been considered in detail.
7 Installation, Commissioning, and Control of TCS
In the initial LIGO setup, the CO2 laser projector pattern is fixed by a mask, with thermal compensation primarily controlled by the power supplied to the two ITMs Common-mode TCS heating is utilized to optimize RF sideband power in the recycling cavity, while a bulls-eye photodetector monitors the pickoff beam size for servo adjustments Conversely, differential-mode TCS heating aims to reduce the unwanted AS_I signal at the dark port However, the exact cause of the TCS-AS_I coupling remains unclear, and the servo gain fluctuates significantly with changes in IFO input power, occasionally even reversing its effect.
The ideal Thermal Control System (TCS) servo should be capable of sensing the spatial profile of the main Interferometer (IFO) beam and dynamically adjusting the actuator's spatial profile to maintain it at a nominal state However, a conceptual design for a thermal compensator that effectively reconfigures its spatial profile without introducing significant noise into the IFO is currently lacking Additionally, there is no existing method to extract information from the IFO beam profile to guide the TCS in applying the appropriate spatial heat pattern to specific mirrors with the correct power This challenge underscores the necessity for dedicated TCS sensors.
Despite the absence of dynamic control over the heater's spatial profile and limited information regarding the thermal phase profile of the ITMs, the Thermal Control System (TCS) performed effectively on initial LIGO Notably, it continued to function well even when the heating of H1 approached nearly half of the anticipated levels for Advanced LIGO.
I NSTALLATION AND C OMMISSIONING
The installation and commissioning phase of TCS will go as follows:
Each core optic and compensation plate is equipped with an absorption map that corresponds to its coating and substrate, accurately aligned with its orientation in the interferometer This absorption data will be integrated into a finite element thermal model to forecast the thermal phase profile under different IFO laser power levels and time intervals The resulting information will inform the design of spatial profiles for the CO2 laser projector, in conjunction with the anticipated shielded ring heater profile Additionally, reflection phase maps of the optics will support the commissioning of dedicated TCS sensors.
2) Design the initial CO2 laser projector profile.
The information from the predicted thermal profiles will be used to design spatial profiles for the CO2 laser projector.
3) Characterize the in-vacuum steering mirrors and telescopes.
At this stage, the effects of distortion and other aberrations can be measured in the optics laboratory, for use later in qualifying the TCS dedicated sensors.
4) Characterize the dedicated TCS sensors.
At this point the TCS sensors can be tested against a reference flat either with or without the in- vacuum optics, as desired.
5) Install the ring heaters and compensation plates with the test mass suspensions.
At this stage, the centering of the CP and the ring heater will be assured.
6) Install the in-vacuum steering mirrors, telescopes, and viewports.
The position of the optical axis within the in-vacuum optics, directed towards the ITMs and BSs, can be accurately measured to assist in aligning the specialized TCS sensors.
7) Install the dedicated TCS sensors.
At this point the mapping of the optic face to the detector plane of the TCS dedicated sensors will be done.
Step 7 is the last stage of the TCS commissioning when access to equipment inside the vacuum chamber is required.
8) Characterize and install the CO2 laser projectors.
The TCS dedicated sensors will enhance projector centering by eliminating the reliance on the red laser diode crosshair projector used in initial LIGO, which will now serve only for rough alignment Instead, a test-pattern mask, potentially a small central crosshair, will be projected onto the CP and detected by the TCS dedicated sensor to ensure accurate alignment.
9) Install the servo electronics for the CO2 laser projectors, TCS dedicated sensors, and ring heaters, and the phase cameras.
From this point forward, the TCS commissioning will require that the interferometer be under vacuum.
10) Adjust the heaters to make sure the TCS sensors and actuators yield results consistent with predictions on individual optics.
This stage is meant to verify end-to-end that a TCS actuator can produce a signal observable by the corresponding TCS dedicated sensor as expected
From this point forward, the TCS commissioning will require some optical power circulating inside the interferometer.
11) Lock the interferometer at low power and measure the self-heating with the TCS sensors; test the compensation with the ring heaters and CO 2 laser projectors.
If the initial estimate of the optimal heating pattern for the CO2 laser projector is inaccurate, it will likely be identified at this stage Utilizing TCS dedicated sensors, phase profiles can be measured to create enhanced heater spatial profiles Additionally, any optics that absorb significantly differently than anticipated from the initial data will also be revealed at this point.
12) Revise the CO 2 laser projector heating profiles and repeat step 11).
The process of increasing the IFO power and advancing the interferometer commissioning will likely involve multiple repetitions, contingent on the current requirements for TCS performance.
We plan to implement a servomechanism to control TCS power levels for various optics, drawing on insights from initial LIGO experiences While a detailed model of interferometer performance is lacking, developing an effective strategy is manageable Our initial approach will utilize dedicated sensors to measure the compensated optic phase profiles, generating an error signal based on their deviation from the cold phase profile This method has previously shown promising results with a scanning CO2 laser projector compensator, as demonstrated by Ryan Lawrence.
D IFFERENTIAL C ONTROL
In the initial LIGO setup, the differential-mode TCS level was selected to maintain a low AS_I signal at the dark port However, Advanced LIGO employs a homodyne readout scheme that eliminates the AS_I signal, shifting the focus of the differential TCS to the dark port power While it is challenging to define the exact performance requirements for the TCS in this context, we anticipate that these requirements will be readily satisfied.
Ryan Lawrence utilized Melody to assess the total power at the dark port, factoring in differential thermal effects between the two arms His findings indicated that most stray light was in higher-order modes, which subsequently increased shot noise at the output photodetector While Lawrence's model was accurate, it lacked considerations for signal recycling, an output mode cleaner, and the homodyne readout scheme, all of which significantly influence Advanced LIGO's sensitivity to differential thermal effects, typically reducing it Additionally, Lawrence did not account for stable recycling cavities, which remain a potential option for Advanced LIGO but are not addressed in this context.
The output mode cleaner represents a major advancement, designed with a finesse ranging from 100 to 1000 and a cavity length of approximately 30 cm For the purposes of this discussion, we will focus on a finesse of 300.
For an exactly antiresonant mode, the power transmittance of the (lossless) output mode cleaner is
In general, the transmissivity is expected to be higher, but for modes not within 5% of a free spectral range of resonance, suppression will be at least 2.8x10^-3 Assuming that no significant higher transverse modes fall within this range, the requirement dictates that no more than 1 mW of dark port light can originate from higher order modes Consequently, this means that the signal recycling mirror can emit a maximum of 357 mW.
The inclusion of the signal recycling mirror introduces additional complexity to the dual-recycled interferometer model, which requires a comprehensive analysis that accounts for thermal effects Preliminary estimates indicate that with a signal recycling mirror transmittance of 0.05, a maximum of 357 mW of junk light can exit the signal cavity, allowing for no more than 7.14 W of junk light to strike the signal recycling mirror.
The impact of the signal mirror on the power buildup of transverse carrier modes remains insufficiently modeled Lawrence's previous work on a thermally compensated fused silica Advanced LIGO, which excluded the signal mirror, demonstrated that junk light levels remained below 1 W, even with a 50% differential absorption between the arms To achieve a mode overlap greater than 99.7% with 2100 W at the beamsplitter, the light from contrast defects must be limited to under 7.14 W Consequently, the ring heater design outlined in section 4.1.2 is expected to meet this critical requirement.
14 Section 3.1.2.4, TCS Design Requirements Document
Figure 19: IFO performance with thermal compensation and no SRM From Lawrence's thesis.
C OUPLING OF T EST M ASS F LEXURE N OISE TO D ISPLACEMENT N OISE
A test mass ring heater alters the radius of curvature of a test mass's high-reflectivity (HR) surface by flexing the mirror This flexure causes the center of the HR surface to shift in relation to the test mass's center of gravity, leading to displacement noise from any fluctuations in the ring heater's power For a comprehensive analysis of this phenomenon, refer to LIGO document T060224-00-D.
Figure 20: Thermoelastic deformation from 1 second of 100 W of barrel heating.
The thermoelastic deformation of the test mass under 1 W, 100 Hz barrel heating is illustrated in Figure 20, which was modeled using COMSOL This model allows for the estimation of flexure noise coupling by analyzing the displacement of the center of the high-reflectivity (HR) face, measured at 4x10^-16 m, in comparison to the mean displacement of the mirror's center of mass, calculated to be 2x10^-16 m.
We require the TCS injected displacement noise to be less than 5x10 -22 m/Hz at 100 Hz, so this 1
To effectively manage W fluctuation, it should be reduced to 2.4x10 -6 W/√Hz Compensating the arm cavity at elevated IFO power levels necessitates delivering 22W of heat to the ETM, which requires a RIN of 1.1x10 -7 /√Hz Utilizing a ring heater will facilitate this process, as its thermal inertia will help to passively stabilize power fluctuations in the input supply.
The full analysis of the flexure, elasto-optic, thermoelastic, and thermorefractive noise couplings in both the CP and the TM can be found in LIGO document T060224-00-D.