Compact Balanced Readout Interferometer (COBRI)

• COBRI is a compact interferometric sensor that combines balanced readout, multi-fringe phase recovery, and low-noise electronics to achieve high-precision displacement sensing.
• It employs deep frequency modulation and quadrature techniques to enable large range operation with robust, absolute phase tracking over many fringes.
• The system enhances suspension control by reducing sensor noise and enabling active damping for both longitudinal and rotational degrees of freedom in precision instruments.

Compact Balanced Readout Interferometer (COBRI) denotes a compact interferometric displacement sensor in which balanced or balanced-like readout, multi-fringe phase recovery, and low-noise electronics are combined to provide large-range local metrology. In the suspension-control literature, COBRI is described as “a sensor currently in development that is based on deep frequency modulation,” intended as an interferometric alternative to shadow sensors for active damping of suspended optics (Weickhardt et al., 24 Jul 2025). Earlier interferometers are presented as concrete realizations or direct blueprints of the same design logic, notably a compact fibre-coupled quadrature Mach–Zehnder interferometer for inertial sensing and precision positioning (Cooper et al., 2017) and a single-component deep-frequency-modulation interferometer smaller than a cubic inch with sub-picometer displacement precision (Isleif et al., 2019).

1. Definition and research setting

COBRI emerges from a specific instrumentation problem: below about $30\,\mathrm{Hz}$, ground-based gravitational-wave detectors are strongly impacted by control-induced displacement noise, and the local displacement sensors used for suspension damping are a major contributor to that noise floor (Weickhardt et al., 24 Jul 2025). In present LIGO/Virgo-type systems, local sensing is dominated by shadow sensors such as BOSEMs, with a noise floor in the range

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$

depending on frequency and variant. COBRI is proposed as a compact interferometric replacement or complement that preserves local damping functionality while reducing sensor noise by orders of magnitude in the relevant band (Weickhardt et al., 24 Jul 2025).

Within this usage, COBRI is characterized by four recurring attributes. First, it is compact: the optical head is intended to be small-footprint, mechanically stable, and compatible with multi-sensor deployment. Second, it employs balanced readout, usually by subtracting complementary photodiode outputs, to suppress common-mode intensity noise and related technical couplings. Third, it is explicitly multi-fringe, so that displacement reconstruction is not limited to a fraction of a fringe. Fourth, it is intended to support auxiliary functions such as absolute ranging and multi-degree-of-freedom sensing in suspension controls (Weickhardt et al., 24 Jul 2025).

The systems-level target is not merely lower readout noise in isolation. The stated objective is improved control of suspended masses, including longitudinal and rotational degrees of freedom, without the penalty that conventional local sensors impose on the interferometer output (Weickhardt et al., 24 Jul 2025). This framing is important: COBRI is best understood as a local metrology architecture for control-limited precision instruments, rather than as a generic interferometer label.

2. Optical architectures and balanced readout

One concrete realization associated with the COBRI concept is the homodyne quadrature Mach–Zehnder interferometer reported in “A compact, large-range interferometer for precision measurement and inertial sensing” (Cooper et al., 2017). That device uses a $1064\,\mathrm{nm}$ low-noise laser, a $2\,\mathrm{m}$ PM fiber, polarization splitting at PBS2 into orthogonally polarized arms of length $L_x$ and $L_y$, recombination at PBS2, and a non-polarizing beamsplitter followed by a quarter-wave plate and a third PBS to generate quadrature outputs. The baseplate is $170\times100\,\mathrm{mm}$, with all optics mounted rigidly on an aluminum baseplate of relatively large thermal mass. In the language of COBRI, this is a compact, fibre-coupled optical head (Cooper et al., 2017).

Its phase variable is

$\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$

and the three photodiode powers are reported as

$$\mathrm{PD1}=\frac{P_{\rm in}}{8}\bigl(1+a\sin\phi_{\rm opt}\bigr),$$

$$\mathrm{PD2}=\frac{P_{\rm in}}{8}\bigl(1+a\cos\phi_{\rm opt}\bigr),$$

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$0

From these, two difference signals are formed: $$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$1

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$2

These differences suppress common-mode dependence on total optical power $$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$3 and fringe visibility $$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$4, and reject laser intensity noise that affects all photodiodes equally (Cooper et al., 2017).

The COBRI development study describes the sensor more generally as “a compact interferometer (in practice a folded Michelson/Mach–Zehnder-like configuration)” combined with deep frequency modulation and balanced readout at the detection stage (Weickhardt et al., 24 Jul 2025). In that description, the optical phase is written as

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$5

with deep frequency modulation introduced through

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$6

leading to a signal of the form

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$7

Balanced readout is implemented as

$$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$8

with the stated purpose of suppressing common-mode laser intensity noise, some environmental perturbations, and background offsets (Weickhardt et al., 24 Jul 2025).

The literature therefore does not restrict COBRI to a single optical topology. A plausible summary is that the term denotes a compact interferometric sensor class whose defining features are balanced or complementary outputs, compact opto-mechanics, and phase reconstruction robust over many fringes.

3. Phase recovery, multi-fringe operation, and absolute ranging

A central property of COBRI is large working range. In the quadrature Mach–Zehnder implementation, the two differential signals provide sine/cosine-like responses over $$\tilde d_\text{shadow} \sim 1~\text{to}~0.04~\mathrm{nm}/\sqrt{\mathrm{Hz}},$$9 of phase, and the phase is reconstructed digitally by computing a four-quadrant arctangent on an FPGA using a CORDIC engine (Cooper et al., 2017). The phase is then unwrapped continuously, so that the displacement readout is linear in the unwrapped phase: $1064\,\mathrm{nm}$0 Because the raw photodiode signals are not used directly as the displacement observable, linearity is maintained over many fringes; in the reported prototype, the displacement working range exceeds $1064\,\mathrm{nm}$1 (Cooper et al., 2017).

Deep frequency modulation interferometry provides a second route to the same goal. In the prism interferometer reported in “Compact multi-fringe interferometry with sub-picometer precision,” the effective modulation index is

$1064\,\mathrm{nm}$2

and the interferometric output is expanded into harmonics weighted by Bessel functions (Isleif et al., 2019). The phase is not reconstructed from a single sinusoid, but from a multi-harmonic fit using Levenberg–Marquardt to recover interferometric phase, amplitude, modulation index, and modulation phase. This is explicitly described as a multi-fringe readout, and the same paper identifies it as providing unambiguous, large-range, absolute phase tracking with only one beam and one optics block per sensor (Isleif et al., 2019).

The 2025 COBRI study treats this multi-fringe property as operationally central. It attributes to COBRI “multi-fringe displacement readout (no ambiguity over many wavelengths)” and “absolute ranging capability,” and states that the experiment is intended to investigate “auxiliary functions, such as absolute ranging, in the context of the 6 degree-of-freedom controls of the suspensions” (Weickhardt et al., 24 Jul 2025). A common misconception is that compact local sensors are relevant only for small fluctuations about a fixed operating point. The cited COBRI literature instead emphasizes recovery after large drifts or lock loss, robust phase tracking across many $1064\,\mathrm{nm}$3 cycles, and absolute determination of top-mass position relative to the sensor head (Weickhardt et al., 24 Jul 2025).

4. Sensitivity, noise budgets, and limiting mechanisms

The quadrature Mach–Zehnder implementation reports a peak displacement sensitivity of

$1064\,\mathrm{nm}$4

at $1064\,\mathrm{nm}$5, and

$1064\,\mathrm{nm}$6

at $1064\,\mathrm{nm}$7, measured in air with the baseplate on rubber feet over $1064\,\mathrm{nm}$8 of data acquisition (Cooper et al., 2017). Its identified noise sources include electronic noise, laser frequency noise corresponding to an effective arm mismatch of $1064\,\mathrm{nm}$9, air currents, temperature fluctuations, table motion near $2\,\mathrm{m}$0, and electrical pickup at $2\,\mathrm{m}$1. The paper states that the total sensitivity is probably limited by electronic noise near $2\,\mathrm{m}$2, and below that by a combination of air currents, temperature fluctuations, and frequency noise (Cooper et al., 2017).

When projected onto a GS‑13 geophone, that readout is sufficiently quiet that the overall inertial sensor would be limited by suspension thermal noise rather than readout noise from $2\,\mathrm{m}$3 to $2\,\mathrm{m}$4 (Cooper et al., 2017). This is a recurring theme in COBRI work: once the optical readout is sufficiently improved, mechanical thermal noise, seismic coupling, actuator noise, and environmental couplings become the dominant constraints.

The DFMI prism interferometer reports displacement noise of approximately $2\,\mathrm{m}$5 between $2\,\mathrm{m}$6 and $2\,\mathrm{m}$7, and tilt noise of approximately $2\,\mathrm{m}$8 for frequencies above $2\,\mathrm{m}$9. Its abstract summarizes the performance more broadly as less than $L_x$0 and $L_x$1 at frequencies below $L_x$2 (Isleif et al., 2019). The same work identifies laser frequency noise, residual amplitude modulation, digitization noise, thermal and mechanical environmental noise, and tilt-to-length coupling of about $L_x$3 as dominant technical limitations, while shot noise is calculated to be below $L_x$4 and therefore not limiting (Isleif et al., 2019).

The suspension-control study adopts a COBRI noise model informed by Cramér–Rao lower bound calculations for deep frequency modulation interferometry, with an $L_x$5 rise at low frequency from incomplete laser frequency-noise suppression and a nearly flat or slowly rising high-frequency plateau from electronics. It also states a peak theoretical displacement sensitivity of order

$L_x$6

At the same time, the modeled suspended-cavity noise budget shows that seismic noise, actuator noise, suspension thermal noise, coating thermal noise, and laser-frequency noise of the reference cavity can dominate the observable cavity motion unless the pre-isolation is improved (Weickhardt et al., 24 Jul 2025).

5. Suspension control, inertial sensing, and precision positioning

In inertial sensing, the intended COBRI coupling is direct optical readout of the relative displacement between a proof mass and the sensor housing. For the GS‑13 example, one end mirror is conceptually replaced by the proof mass or reference mass of the commercial inertial sensor, while the other end mirror remains rigidly attached to the housing or ground, so that $L_x$7 becomes the mass-to-housing displacement (Cooper et al., 2017). The same study also projects performance to a Watt’s linkage with $L_x$8, $L_x$9, and $L_y$0, emphasizing that improved mechanics are necessary once the readout is no longer limiting (Cooper et al., 2017).

The most detailed proposed application is local suspension control on two HAM Relay Triple Suspension systems. There, COBRIs are to be mounted opposite each BOSEM on the top mass, while the BOSEM remains as actuator and reference sensor, enabling a direct comparison between BOSEM-based and COBRI-based local sensing using the same plant and the same voice-coil actuators (Weickhardt et al., 24 Jul 2025). The suspended test masses form a $L_y$1 optical cavity of finesse $L_y$2, and the differential cavity length relative to a $L_y$3 monolithic reference cavity is used as the figure of merit (Weickhardt et al., 24 Jul 2025).

The simulations show that, with the current seismic isolation of the VATIGrav facility, replacing BOSEMs by COBRIs yields a factor of approximately $L_y$4 improvement in cavity length stability in the $L_y$5–$L_y$6 band (Weickhardt et al., 24 Jul 2025). The same study argues that a more decisive demonstration requires pre-isolation improved by about $L_y$7–$L_y$8 orders of magnitude across $L_y$9–$170\times100\,\mathrm{mm}$0, together with a conservative one-order-of-magnitude reduction in DAC range; under those conditions, the difference between BOSEM- and COBRI-damped systems is expected to increase to at least an order of magnitude around $170\times100\,\mathrm{mm}$1 (Weickhardt et al., 24 Jul 2025).

Rotational control is especially significant. The paper states that BOSEM self-noise lies above the measured rotational motion of the table and suspension above about $170\times100\,\mathrm{mm}$2, so BOSEM-based rotational damping would inject rather than remove noise. COBRI pitch noise, by contrast, lies below the measured rotational motion, enabling active damping of pitch and yaw without the self-noise penalty that presently prevents BOSEM-based rotational control (Weickhardt et al., 24 Jul 2025). This suggests that COBRI’s main system-level value may be as much in enabling new control topologies as in reducing longitudinal sensor noise alone.

6. Related interferometric lineages, extensions, and constraints

Several adjacent lines of work illuminate what COBRI requires and what it does not automatically solve. Balanced homodyne readout in a Michelson–Sagnac optomechanical interferometer demonstrated arbitrary quadrature access, a readout noise of $170\times100\,\mathrm{mm}$3 around a $170\times100\,\mathrm{mm}$4 membrane resonance, and operation $170\times100\,\mathrm{mm}$5 times below the peak value of the SQL curve in imprecision alone (Kaufer et al., 2012). That work is not a suspension-control COBRI, but it establishes the relevance of balanced readout, local-oscillator phase control, and quadrature selectivity for compact interferometric sensors.

Dual balanced readout at the symmetric and antisymmetric ports of a Michelson interferometer demonstrated experimental subtraction of scattered-light noise with a reduction of $170\times100\,\mathrm{mm}$6, and emphasized that there is no theoretical suppression limit other than shot noise (Lohde et al., 2024). At the same time, the reported limitations—imperfect quadrature locking, electrical crosstalk, non-identical scattered-light coupling, and readout noise above the expected shot-noise level—show that balanced multi-port readout is not self-validating. It depends critically on phase control, mode matching, and low-noise electronics (Lohde et al., 2024).

Balanced readout also introduces stringent implementation requirements on the local oscillator. For advanced gravitational-wave detectors, local-oscillator amplitude noise must satisfy

$170\times100\,\mathrm{mm}$7

and differential path motion between signal and local-oscillator paths must satisfy

$170\times100\,\mathrm{mm}$8

at $170\times100\,\mathrm{mm}$9 (Steinlechner et al., 2015). This is directly relevant to any COBRI variant using external balanced homodyne rather than self-referenced differential outputs.

Other antecedents reinforce the same compact balanced-readout design program. A quasimonolithic unequal-arm Mach–Zehnder interferometer with balanced dc readout achieved laser-frequency-noise levels below $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$0 at $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$1 and demonstrated the LISA pre-stabilization requirement of $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$2 down to $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$3 (Gerberding et al., 2016). A compact heterodyne interferometer with spatially separated beams reported picometer-level displacement sensitivities in air over frequencies above $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$4, higher sensitivity of $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$5, higher thermal stability by a factor of two, and periodic-error-free performance relative to a commercial system (Joo et al., 2020). A three-output integrated photonic tricoupler demonstrated a throughput of $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$6, flux splitting ratios between $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$7 and $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$8 over a $\phi_{\rm opt}=\frac{4\pi(L_x-L_y)}{\lambda},$9 bandpass, and instantaneous complex visibility and group delay estimation from a compact beam combiner (Hansen et al., 2021). These devices are not identical to suspension-control COBRIs, but they show that compactness, balanced or multi-port readout, and direct complex phase retrieval form a coherent technical lineage.

A recurring misconception is therefore that COBRI names a single immutable optical layout. The cited work suggests a narrower common denominator: compact opto-mechanics, balanced or complementary output channels, digital phase reconstruction over many fringes, and explicit attention to low-frequency technical couplings. Equally, the literature rejects the converse misconception that a superior readout alone determines sensor performance. Across the cited studies, thermal noise, tilt-to-length coupling, local-oscillator path noise, digitization limits, actuator noise, and seismic pre-isolation remain decisive once interferometric readout noise is reduced (Cooper et al., 2017, Isleif et al., 2019, Lohde et al., 2024, Weickhardt et al., 24 Jul 2025).