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Micromachines 2026 , 17 , 592 29 of 34 Finally , the data exposes a critical divergence between sample efﬁciency and true temporal efﬁciency . Although Global BO consistently requires the fewest physical mea- surements (…

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5.2.2. Scenario 2: LS-NH (Low-Speed, No Hysteresis)

Algorithmic hysteresis compensation effectively eliminates the reset-to-zero over-

head, although hardware actuation speeds remain inherently slow. This conﬁguration

successfully isolates the speciﬁc operational beneﬁts of software-based compensation. With

hysteresis effectively mitigated in software, alignment times improve across all methods

(Table 3). Nevertheless, Fix-Grad maintains its operational dominance. Var-Grad provides

a marginal speed advantage of roughly 2 a.u., but its lower reliability presents an unfa-

vorable speed-versus-yield trade-off. Although the removal of physical reset maneuvers

improves the relative viability of Bayesian methods compared to the LS-H scenario, their

computational overhead keeps them slower than gradient-based alternatives, solidifying

Fix-Grad as the deﬁnitively recommended strategy.

5.2.3. Scenario 3: HS-H (High-Speed with Hysteresis)

Representing typical production conditions, this scenario pairs rapid hardware kine-

matics with uncompensated hysteresis. Evaluating algorithmic efﬁcacy under these con-

straints is vital for industrial systems where implementing feedforward compensation

remains impractical. In this realistic high-volume conﬁguration, Fix-Grad is strongly rec-

ommended when alignment reliability is paramount, maintaining peak success rates while

remaining highly competitive in execution speed. Var-Grad should be restricted to prelimi-

nary screening applications where occasional failures are an acceptable trade-off for rapid

alignment. Notably, this scenario highlights a critical limitation of the Global BO approach:

without cross-scan initialization, pure probabilistic exploration struggles to resolve the

hysteresis-distorted landscape efﬁciently, resulting in both the lowest reliability and longest

execution time among the optimization methods.

5.2.4. Scenario 4: HS-NH (High-Speed No Hysteresis)

This ideal regime couples rapid hardware kinematics with effective feedforward hys-

teresis compensation [

]. Representing the gold standard for production deployment,

this conﬁguration highlights the ultimate capabilities of the algorithms. Fix-Grad is deﬁni-

tively recommended, delivering an optimal balance of high reliability and rapid alignment

to effectively mitigate throughput bottlenecks [

]. While Var-Grad achieves the absolute

fastest alignment time (approaching 1 a.u.), its persistent 9.7% failure rate remains a lim-

iting factor for strict production environments. Conversely, despite requiring the fewest

physical measurement steps, the substantial computational overhead of GP ﬁtting severely

inﬂates the temporal cost of the Global BO method, rendering it unsuitable for high-volume

environments demanding both absolute reliability and sub-second speed.

5.3. Cross-Scenario Performance Analysis

A cross-scenario comparison reveals several critical insights. First, the Fix-Grad

algorithm demonstrates exceptional robustness, consistently achieving 95.8% reliability

across all speeds and hysteresis conditions. Conversely, Global BO is most sensitive to

uncompensated hysteresis: in the LS regime, reliability drops from 93.1% to 88.9% (

−

4.2%),

and in the HS regime, from 90.3% to 88.9% (

−

1.4%), while its alignment time inﬂates by

92%, rendering it problematic without active feedforward compensation.

Hardware kinematics and hysteresis mitigation drastically impact throughput. Transition-

ing from low-speed to high-speed regimes accelerates Fix-Grad alignment by 14.6

(from 20.95

to 1.44 a.u. without hysteresis) and 21.9

(from 72.47 to 3.32 a.u. with hysteresis). Managing

hysteresis via the mandatory reset-to-zero strategy roughly doubles execution time across

all algorithms (detailed in Table 3). Importantly, despite this severe temporal penalty, final

positioning accuracy consistently exceeds 98%, validating the open-loop control architecture.

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Finally, the data exposes a critical divergence between sample efﬁciency and true

temporal efﬁciency. Although Global BO consistently requires the fewest physical mea-

surements (24 steps), its substantial computational overhead for Gaussian Process updates

results in a longer total execution time (2.24 a.u.) than Fix-Grad (1.44 a.u. across 34 steps).

Consequently, sample efﬁciency alone is a misleading metric for evaluating high-volume

production throughput.

5.4. Impact of Operating Speed

High-speed operation is essential for achieving production-viable throughput, as it

drastically reduces per-die optical alignment time. Using the Fix-Grad algorithm as a

benchmark, execution time decreases from 72.47 a.u. in the worst-case low-speed hysteretic

regime (LS-H) to 20.95 a.u. in the low-speed non-hysteretic regime (LS-NH), 3.32 a.u. in

the high-speed hysteretic regime (HS-H), and ultimately 1.44 a.u. in the ideal high-speed

non-hysteretic regime (HS-NH). Transitioning from low-speed to high-speed operation

therefore yields a 14.6-fold acceleration in the absence of hysteresis and an even larger

21.9-fold speedup when hysteresis is present.

The practical signiﬁcance of this acceleration becomes clear at the wafer scale. For a

standard 300 mm wafer containing 200 PIC dies, the total optical alignment burden rises to

approximately 14,500 a.u. in the LS-H regime, which is clearly impractical for manufactur-

ing. Under realistic high-speed operation with hysteresis (HS-H), this total is reduced to

approximately 664 a.u., already representing a major improvement in throughput. In the

ideal HS-NH regime, the total falls further to approximately 288 a.u. per wafer.

To relate these normalized values to real production conditions, we note that the ideal

Fix-Grad alignment time of 1.44 a.u. is consistent with the sub-second per-die optical cou-

pling times reported in state-of-the-art automated photonic test systems [

]. Under this

interpretation, the HS-NH regime corresponds to full-wafer optical alignment in a matter

of minutes, whereas the LS-H regime would translate into a multi-hour process devoted

only to optical alignment. This difference clearly shows that high-speed actuation is not

merely beneﬁcial, but fundamentally necessary for meeting the throughput requirements

of high-volume PIC and co-packaged optics manufacturing [1,3].

Overall, these results validate the importance of integrating high-speed piezoelectric

drive electronics directly into the probe-card architecture. They also show that, when

combined with an efﬁcient search strategy such as Fix-Grad, the Eclipse Dynamic platform

can achieve alignment times consistent with the fastest per-die coupling results reported in

the recent literature [10,11].

5.5. Impact of Hysteresis

Hysteresis imposes a severe temporal penalty due to mandatory reset-to-zero motions,

inﬂating high-speed execution times by 130% for the Fix-Grad algorithm (from 1.44 to

3.32 a.u.) and by 92% for the Global BO method (from 2.24 to 4.29 a.u.). Despite this

near-halving of throughput, robust algorithms maintain highly stable alignment quality:

Fix-Grad retains a constant 99.4% accuracy and 95.8% reliability regardless of hysteresis.

Conversely, the Global BO approach experiences a reliability degradation from 90.3% to

88.9%, indicating that uncompensated hysteresis distorts the coupling landscape sufﬁciently

to trap pure probabilistic exploration in local maxima. Ultimately, the business case for

implementing feedforward hysteresis compensation, such as inverse P-I models [

], is

highly compelling. Mitigating these nonlinearities effectively doubles system throughput

and tester capacity, thoroughly justifying the initial software development investment.

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5.6. Statistical Validity: Data Proﬁles Versus Averages

Data proﬁle analysis (Figures 9 and 10) conﬁrms the above mentioned ﬁndings [

For instance, while Var-Grad exhibits a misleadingly low average step count (26.1), its

data proﬁle reveals a premature plateau at a 90.3% success rate, indicating fundamental

algorithmic limitations rather than mere parameter mistuning. Conversely, the steep proﬁle

slopes of the Fix-Grad and Local BO algorithms demonstrate rapid, highly consistent

convergence. From a practical manufacturing perspective, these proﬁles explicitly quantify

worst-case performance and failure rates, directly informing throughput modeling by

accounting for severe manual intervention overhead.

5.7. Comparison to State-of-the-Art

Contextualized against recent automated alignment benchmarks that report multi-

second per-die execution times [

], the evaluated methods demonstrate highly com-

petitive, sub-second performance. Operating entirely in an open-loop conﬁguration, the

Fix-Grad algorithm achieves a rapid 1.44 a.u. alignment time alongside 95.8% reliability

and 99.4% accuracy. Furthermore, experimental validation of the Local BO method yields

a 100% success rate and a 3–4

speedup (99.87 a.u.) over exhaustive reference scans.

Crucially, these capabilities are realized without closed-loop position feedback, relying

instead on computationally efﬁcient algorithmic optimization, where even GP ﬁtting runs

in real-time on embedded systems and robust feedforward hysteresis compensation [

This performance underscores a critical innovation: deploying sophisticated algo-

rithms to effectively compensate for simpliﬁed hardware mechanics. By eliminating the

necessity for bulky external positioning equipment, this approach enables the cost-effective

integration of optical alignment capabilities directly into the probe card. For high-volume

PIC manufacturing [

], this integrated architecture provides a profound advantage. It

inherently facilitates simultaneous multi-channel parallel testing, delivering multiplica-

tive throughput enhancements that scale signiﬁcantly beyond standard per-die speed

improvements [5,12].

5.8. Limitations and Future Work

Several avenues warrant further investigation to advance automated wafer-level

photonic testing. Future research will explore data-driven control architectures to further

enhance system throughput. Speciﬁcally, replacing analytical hysteresis models with

Long Short-Term Memory (LSTM) networks is expected to yield higher accuracy by better

capturing deep, history-dependent piezoelectric behaviors. Concurrently, Reinforcement

Learning (RL) agents offer the potential to adaptively counteract complex mechanical wear

and drift over the lifespan of the probe card, outperforming static algorithms for dynamic

ﬁne-stage optimization.

Additionally, expanding these methods to multi-ﬁber array alignments will require

strategies to balance peak loopback transmission with channel uniformity and crosstalk

limits across the array. Because the FAU moves as a rigid block, optimizing a single

channel can induce misalignment on peripheral channels due to planar tilt. Utilizing

the differential Y1/Y2 piezoelectric actuators for precise rotational tilt compensation will

be essential in navigating these multi-channel compromises. Finally, standardizing chip

layouts, such as ﬁxing input/output port offsets and reference waveguide lengths across

different PIC designs, would signiﬁcantly narrow the spatial bounding required for search

algorithms, accelerating the cross-scan initialization phase for both Bayesian and Gradient

methodologies. To mitigate the initialization challenges observed in Bayesian methods,

historical wafer data can also be leveraged to generate predictive spatial probability maps,

drastically reducing initial search areas. Furthermore, online learning and advanced sensor

https://doi.org/10.3390/mi17050592