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Micromachines 2026 , 17 , 592 30 of 34 5.6. Statistical V alidity: Data Proﬁles V ersus Averages Data proﬁle analysis (Figur es 9 and 10 ) conﬁrms the above mentioned ﬁndings [ 18 ]. For instance, while V ar-Grad exhibit…

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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

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data imputation techniques [

] must be developed to maintain alignment robustness

against real-time probe drift and intermittent signal degradation.

Transitioning these methodologies to high-volume manufacturing demands broader

experimental validation across diverse foundries, device architectures, and multi-ﬁber

arrays. In such high-dimensional optimization landscapes, the algorithmic hierarchy may

shift favorably toward Bayesian surrogate models [

]. Crucially, these sub-second

alignment strategies must be seamlessly integrated into double-sided test cells to meet

the aggressive throughput demands of CPO production ﬂows [

]. Finally, coupling

operational alignment metrics with digital twin frameworks and transformer-based sensor

placement [

] will enable robust structural health monitoring, facilitating predictive

maintenance and extending probe card lifespans in demanding industrial environments.

6. Conclusions

This paper presented a comprehensive evaluation of alignment optimization tech-

niques for wafer-level photonic integrated circuit testing, utilizing the Technoprobe Eclipse

Dynamic probe card system. Through robust experimental validation and extensive simu-

lations spanning diverse operating regimes, incorporating varying actuation speeds and

hysteresis conditions, this study systematically benchmarked seven alignment algorithms.

The results unequivocally establish the Fix-Grad algorithm as the optimal solution for

high-volume manufacturing. Across all evaluated conditions, this approach demonstrated

exceptional robustness, consistently delivering a 95.8% reliability rate and 99.4% align-

ment accuracy.

Transitioning to high-speed actuator drive electronics is essential for production via-

bility, providing a 14.6–21.9

throughput improvement over low-speed operation (Table 3).

In the ideal high-speed, hysteresis-compensated regime, the Fix-Grad algorithm achieved a

rapid alignment time of 1.44 a.u. per die. While uncompensated hysteresis approximately

doubles this execution time, algorithmic mitigation strategies successfully preserve ﬁnal

measurement quality without requiring complex closed-loop positioning feedback. Alter-

native methods presented speciﬁc trade-offs—the Var-Grad technique offered the fastest

alignment (1.18 a.u.) but suffered a higher failure rate of 9.7%, rendering it suitable only for

non-critical screening. Furthermore, despite high sample efﬁciency, BO approaches exhib-

ited excessive computational overhead and heightened sensitivity to hysteresis, limiting

their viability for strict production environments.

From a production perspective, data proﬁle analysis conﬁrms that the high reliability

of the Fix-Grad method limits manual operator intervention to just 4.2% of tested dies. For a

standard 300 mm wafer containing 200 dies, this integrated architecture facilitates complete

optical characterization in approximately 288 to 664 a.u., depending on the extent of active

hysteresis compensation. By achieving highly reliable optical alignments entirely through

open-loop control, this system matches or exceeds the performance metrics reported in

recent literature [

]. Crucially, embedding this capability directly into the probe card

eliminates the need for bulky external positioning stages, signiﬁcantly reducing overall

equipment footprint and enabling the parallel multi-channel testing required for emerging

CPO architectures [1,3].

Future research will focus on advancing data-driven control strategies to further

enhance system throughput and absolute accuracy. Key initiatives include implementing

Long Short-Term Memory networks to replace analytical models for history-dependent

hysteresis compensation, alongside deploying Reinforcement Learning agents to adaptively

counteract complex mechanical irregularities. Additionally, leveraging historical wafer

data to generate predictive spatial heatmaps will heavily optimize search initialization

parameters. Expanding these methodologies to accommodate simultaneous multi-ﬁber

https://doi.org/10.3390/mi17050592