A. Purpose and requirements

The test mass simulator should allow optical pathlength noise measurements to verify accuracy for a well aligned test mass, which means the returned beam is misaligned to the reference beam by up to 10 μrad. In addition to that, a working interferometer readout should be demonstrated for misalignments up to 500 μrad.

The purpose of the telescope simulator is to

We allow for a 10% increase of the requirements by test mass simulator and telescope simulator, respectively.

B. Design considerations

Tilt actuators are required in the telescope simulator for two purposes:

For both purposes, four degrees of freedom are required each. This is achieved by using pairs of mirrors on tip-tilt mounts, of which the first one is used to set the reflection point on the second one, which in turn sets the direction of the beam.

In the test mass simulator for the LISA technology package (LTP) it was observed that PZT stacks only fulfill the LTP length noise requirement for low actuation voltages not sufficient for the complete angle range. Hence, we restricted the choice to those commercially available actuators that do not need a voltage applied to them to stay at an arbitrary angle (set-and-forget devices). Here, the AG-M100N-V6 by Newport was chosen as baseline actuator.

The requirements on the RX beam generated by the telescope simulator restrict its power to about 300pW being detected in the science interferometer. Such small light powers are not detectable by IR-viewer cards commonly used to trace the beam path of IR laser beams. The photo diodes to be used in the science interferometer also exhibit a dark current higher than the current that would be generated by a beam of this light power, also rendering them useless in alignment of this beam.

These properties of the beam and possible detectors show that no signal can be produced to guide the alignment. The only remaining alternative for alignment is to scan the beam across all possible angles and positions and wait for a “by chance” alignment of the two interfering beams within 500 μrad to allow for efficient heterodyne detection and the generation of differential wavefront sensing (DWS) alignment signals [9], [10]. Obviously, this would be a lengthy and cumbersome procedure which calls for a better way of aligning the two beams.

One way to achieve a better alignment is to increase beam power during the alignment stage and then reduce light power afterwards with as little change of geometry and alignment of the RX beam as possible. This allows to detect the beam using conventional methods (IR viewer card and DC-current of photodiode) during the alignment phase and to switch over to heterodyne detection and the use of DWS signals enabled through this pre-alignment.

Further information on design and construction of test mass and telescope simulator can be found in [11].

C. Layout

Figure 8 shows the layout of the test mass and telescope simulator. It defines the positions of all optics to be bonded on the Zerodur base plate using hydroxide-catalysis bonding [12] to provide the necessary stability. Due to the adjustable optics the tolerances on these positions are sufficiently loose to enable the use of a template for the positioning during the bonding process which greatly eases and speeds up the building process.

Fig. 8.

Schematic layout of test mass and telescope simulator

The test mass simulator consists of optical components TMSim1 and Mtm. A pick-up mirror will be placed on the LISA OB between PBS2 and the out-of-plane mirror to send light to mirror TMSim1 that reflects the light to mirror Ttm. The latter uses a reflective gold coating and is placed on a tilt actuator and linear actuator to simulate the test mass. This actuator assembly is described in more detail in Sec. IV-D.

All other components on the Zerodur baseplate belong to the telescope simulator, that is described in the following. The mainly s-polarised output beam from the Fibre Injector Optical Subassembly (FIOS) Telsim in the upper right corner is reflected from polarising beam splitter PBS101 to clean the polarisation. Beam splitter BS101 splits the beam into two equal parts. One part is magnified by lens1 and lens 2 to 5 mm diameter and reflected by mirrors M4 and M3 (45° angle of incidence). Beam combiner BS6 reflects 1% of the power towards the out-of-plane mirror Mup that sends the RX beam towards the science interferometer on the optical bench. M4 and M3 are mounted in actuator assemblies described in Section IV-D below. They are used to align the RX beam to the science interferometer. The other part of the beam is reflected by mirrors M101 and M102 (41.5° angle of incidence) and directed to beam combiner BS103. There, the beam from the Telsim FIOS interferes with a fraction of the TX beam from the optical bench. One percent of the p-polarised TX beam is reflected by BS6, reduced in diameter by lens2 and lens1, transmitted through PBS102 and rotated to s polarisation by half-wave plate HWP1. The interference signals of TX beam and RX beam are detected by photo detectors PD1 and PD2. Mirrors M101 and M102 are used to align the transponder interferometer.

A second FIOS, FIOS com, has been placed in the central upper part. It is used for commissioning of the telescope simulator. Its s-polarised output beam is split by BS104 into two parts. The reflected part propagates towards BS6. For commissioning a mirror and quarter-wave plate will be placed between M3 and BS6, that reflect all light back and rotate its polarisation by 90°, such that it is transmitted through PBS102 and interferes at BS103 with light from FIOS Telsim. The part transmitted through BS104 is interfered at BS106 with light from FIOS Telsim. The interference signals in this commissioning interferometer are detected by photo detectors PD3 and PD4. Polarisation cleaning for the light from FIOS com is performed by PBS102 and PBS105. For commissioning, the beam path between BS102 and BS104 has to be blocked. This will be achieved by insertion of a mirror that reflects the light coming from FIOS Telsim to the space between beam dumps BD1 and BD2 where an additional beam dump will be placed.

A fraction of the power emitted from FIOS Telsim and FIOS com is detected by photo detectors behind BS107 and BS105, respectively, to monitor and or stabilise the output power from the FIOSes.

D. Actuator assemblies

The optical paths on telescope and test mass simulator must be stable to for the temperature noise during mesurements (n_T(f), cf (1)). In order to achieve stable mirror positions, the tilt actuators for mirrors M3, M4, M101, and M102, and the tilt and linear actuators for the test mass mirror, Mtm, have been mounted on temperature-compensating brass mounts. Figure 9 shows a side view of the assembly for the test mass simulator. The linear actuator (AG-LS25V6 by Newport) is screwed onto the brass mount. It translates the tilt mount (AG-M100N-V6 by Newport) that is screwed on top of it to the left and right. A steel adapter plate with the mirror attached to it is glued to the front side of the tilt mount (facing to the right in Fig. 9) The assembly has been designed to keep the mirror front surface at the same position when the temperature varies. The brass mount has three spring leaf-shaped feet, that are glued to the telescope simulator baseplate. When the length of the brass mount changes with temperature, the two feet at the position of the mirror (only one if visible in Fig. 9) stay in position. The foot at the back then bends. The distances a, b, c, d and the thermal expansion coefficients of the respective materials have been chosen, such that the mirror surface stays at the same location. More precisely, for given materials and given distances a, c, and d we will adjust the thickness b of the steel adapter plate to fine-tune the thermal expansion coefficient of the actuator assembly. We aim to achieve .

Fig. 9.

Side view of actuator assembly

The actuator assemblies for mirrors M101, M102, M3, and M4 use a metal adapter instead of the linear actuator shown in Fig. 9.

E. Performance prediction

In this section we predict the pathlength noise performance of the telescope simulator in combination with the optical bench. We also provide the data required to predict the performance in commissioning mode and of optical bench and telescope simulator individually.

1) Local noise sources: First, we consider noise sources that are local to an interferometric readout: shot noise, electronic noise, and relative power noise. They add to the signal at the heterodyne frequency and degrade the interferometric pathlength measurement. Given a signal and a noise of an interferometer readout, its pathlength noise Δs is given by

where λ is the laser wavelength. We consider the signal and the noise from both ports of the interferometer, i.e. from the combined signals of two quadrant photodiodes with four segments each. The rms signal of the combined photocurrents (in A) is given by

where η is the efficiency of the photodiodes, γ the mode overlap (heterodyne efficiency) of the interfering beams and P_sig and P_lo are the signal and local oscillator power before the recombination beamsplitter, respectively. The shot noise, electronic noise, and relative power noise of the combined photocurrents in are given by

where q_e is the elementary charge, n_el is the electronic noise per QPD segment, and n_RPN is the relative power noise of signal and local oscillator beam. We use and in the following.

Inserting (3) and (4), (5), (6) into (2) yields the pathlength noise due to shot noise, electronic noise and relative power noise for interferometer I.

These three noise sources are independent and hence add quadratically. Their combined pathlength noise Δs_L(I) is given by

The optical powers of signal beam and local oscillator beam are listed in Table I. Tables II and III summarise the parameters and constants used in this and the following sections.

TABLE I

Total Optical Powers Before Recombination Beamsplitters

TABLE II

Quantities Used for Performance Prediction.

TABLE III

Constants and Parameters Used for Performance Prediction; Coefficient of Thermal Expansion CTE, Fused Silica FS

We include a further source of pathlength noise that is caused by the point ahead angle mechanism (PAAM) [2] on the optical bench. Optical pathlength noise generated by the PAAM is required to be below Δs_PAAM.

This requirement has been verified experimentally [2].

2) Temperature-related local noise sources: The selected actuators show a coupling from temperature to angle. When reflection point and rotation point do not coincide, the distance l between the two (in a single actuator axis) transforms temperature driven tilts into optical pathlength changes. This pathlength noise Δs_rot for a single actuator axis is given by

where ϕ is the angle of incidence and the angle change per temperature change. The derivation of the factor 2 cos ϕ can be found in [13, pp. 102]. This coupling from temperature to pathlength in the tilt actuator requires to minimise the leverarm l, when the pathlength noise of the test mass interferometer is to be characterised. This will be achieved by replacing the linear actuator by a metal adapter of lower height. We assume that we can keep l ≤ 2 mm both in the test mass simulator as well as in the actuators in the telescope simulator.

Optical pathlength noise due to thermal expansion of the actuator assemblies Δs_Act is given by

where is the expansion coefficient of the actuator assemblies.

3)Noise sources coupled to two interferometers: Some noise sources couple via a path imbalance in the length measurement. Interferometric testing of the LISA optical bench requires to read out two interferometers simultaneously. In this case, the coupling factor is given by a length difference between the two interferometers. In this section we discuss the relevant length differences and allocate them to either optical bench or telescope simulator. We quantify the influence of laser frequency noise, thermal expansion of the setup (thermoelastic noise) and temperature-driven pathlength changes in fused silica (thermo-optic noise) on the length measurement.

Optical pathlength noise due to thermo-optical noise within fused silica Δs_FS is given by

where ΔT is the temperature noise, OPD_FS the effective imbalance in fused silica, α_FS the coefficient of thermal expansion of fused silica, n_FS its refractive index, and the change in refractive index with temperature. The −1 in (12) takes into account, that although a temperature increase increases the geometrical path through fused silica (for a positive α_FS) but at the same time decreases the pathlength in vacuum.

Optical pathlength noise due to thermo-elastic noise of Zerodur Δs_Z is given by

where OPD_Z and α_Z are the path imbalance and coefficient of thermal expansion of Zerodur.

Optical pathlength noise due to laser frequency noise Δs_freq is given by

where c is the speed of light and Δf is the laser frequency noise. Figure 10 shows a schematic view on optical bench and telescope simulator. The TX laser is input to the optical bench, the RX laser is input to the telescope simulator. On the optical bench the science interferometer is shown (BS17), on the telescope simulator the transponder interferometer is shown (BS103). We define path imbalances ΔL_S and ΔL_T between TX and RX laser in science and transponder interferometer, respectively.

Fig. 10.

Schematic view of optical bench and telescope simulator for noise partitioning.

Table IV lists the endpoints of L_TS, L_RS, L_TT and L_RT and all other lengths to be used in this section.

TABLE IV

Pathlength Imbalances and Their Endpoints; CF. Fig. 10

We do not consider the lengths between TX laser and BS13 and RX laser and BS101 because they are common to science and transponder interferometer and hence cancel in the difference of the two. For measurements utilising science and transponder interferometer, the effective length imbalance ΔL is given by

By inserting (15), (16), (18) and (19) into (17)

we find

with

We have partitioned the effective path imbalance ΔL into a part on the optical bench (ΔL_OB) and a part on the telescope simulator (ΔL_TS). This scheme was used to produce the effective path imbalances on Zerodur and in fused silica as listed in Table V.

TABLE V

Effective Path Mismatch on Zerodur and in Fused Silica; Optical Bench OB, Telescope Simulator TS, Transponder Mode Transp., Commissioning Mode Comm.

4) Combinations of noise sources: In this section we combine the individual noise sources discussed in the previous sections. We assume, all actuator assemblies are identical and exhibit the same temperature noise. Then their pathlength noises add linearly. In the horizontal axis the pathlength noises of M101 and M102 and M3 and M4 cancel each other. In the vertical axis the noises add up:

The factor of two outside the round brackets in (23) takes two actuators each into account.

The same is true for the combined effect of longitudinal actuator noise with temperature on the optical pathlength noise Δs_Act,all:

Now we combine the noise sources discussed previously. Optical pathlength noise associated with the telescope simulator Δs_TS is given by

Depending on what path imbalance data from Table V is used, both the pathlength noise performance of the telescope simulator in transponder mode or in commissioning mode can be predicted.

The noise attributed to the optical bench Δs_OB is given by

Finally, we combine the noise sources of optical bench and telescope simulator and obtain

for the noise of optical bench and the telescope simulator in transponder mode Δs_OB+TS.

Figure 11 shows this predicted pathlength noise performance over temperature noise. For temperature noise below the combined noise is below the requirement. For higher temperature noise thermo-optic noise in fused silica is the dominant noise source followed by electronic noise and shot noise in the science interferometer.

Fig. 11.

Performance prediction for optical bench and telescope simulator as function of temperature noise.

5) Frequency dependencies: In Fig. 11 we have considered pathlength noise as function of temperature noise. Now we fix the temperature noise to a specific value and look at the frequeny dependencies of the noise contributions.

Pathlength noise due to electronic noise, relative power noise and shot noise has a uniform frequency distribution. We can use (8), (9), (7), and (10) for a fixed temperature noise without modification.

For the local temperature-dependent noise sources tilt coupling Δs_rot and thermal expansion Δs_Act of actuator assemblies we define an additional noise shape u_M(f)

that we multiply with (23) and (24). We use a temperature noise of as approximation to the measured temperature noise shapes shown in Fig. 4.

For the pathlength noise due to the PAAM, Δs_PAAM, and frequency noise induced pathlength noise, Δs_freq, we multiply (11) and (14) with the shape factor u_PL(f).

For pathlength noise on Zerodur, Δs_Z, and pathlength noise in fused silica, Δs_FS, (13) and (12) are multiplied with u_M(f).

Figure 12 shows the resulting predicted pathlength noise as function of frequency for temperature noise. Since we have demonstrated such temperature noise in the environment foreseen for LISA optical bench testing it seems possible to verify pathlength noise performance of the science interferometer within requirements. At about 3 mHz the pathlength noise might be slightly higher, depending on the temperature noise during the measurements.

Fig. 12.

Performance prediction for optical bench and telescope simulator as function frequency for temperature noise.