🔬 optics

Temperature in Glass Slides: measurement using Phase Sensitive Optical Coherence Tomography and Computational Modeling

This paper demonstrates that phase-sensitive optical coherence tomography (PhS-OCT), supported by computational modeling, enables precise, contactless, and spatially resolved temperature sensing in transparent solids like glass with a sensitivity of 12.4 nm/°C and sub-10 nm stability.

Original authors: Jose M. Folgueiras, Lucas G. Chej, Luis L. Zurdo, Alejandro G. Monastra, Eneas N. Morel, Maria F. Carusela, Jorge R. Torga

Published 2026-03-20

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CC BY 4.0

Original authors: Jose M. Folgueiras, Lucas G. Chej, Luis L. Zurdo, Alejandro G. Monastra, Eneas N. Morel, Maria F. Carusela, Jorge R. Torga

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a standard, cheap glass microscope slide—the kind you'd find in any school science lab. Now, imagine that this piece of glass is secretly a super-precise thermometer that doesn't need batteries, wires, or even touching the thing it's measuring.

That is exactly what this paper is about. The researchers figured out how to turn a simple piece of glass into a high-tech temperature sensor using a special kind of "light radar."

Here is the breakdown of how they did it, using some everyday analogies:

1. The "Light Radar" (Phase-Sensitive OCT)

Think of Optical Coherence Tomography (OCT) like a bat using echolocation, but instead of sound, it uses light. It shoots a beam of light at an object and listens for the echo to figure out how far away the object is.

Usually, this "light radar" is good at measuring distance to within a hair's width (micrometers). But the researchers used a super-advanced version called Phase-Sensitive OCT.

The Analogy: Imagine you are trying to measure the height of a stack of paper. A normal ruler might tell you the stack is 10mm tall. But this special "light radar" is so sensitive it can tell you if you added one single grain of sand to that stack. It can detect changes in distance as small as one nanometer (that's one-billionth of a meter, or about 1/100th the width of a human hair).

2. The "Glass Sandwich" Trick

The researchers didn't just measure the glass from the outside. They treated the glass slide like a sandwich.

Light hits the top of the glass and bounces back.
Light also travels through the glass, hits the bottom, and bounces back.
The machine measures the tiny difference in time (or distance) between those two bounces. This is called the Optical Path Difference (OPD).

3. Why Heat Changes the "Sandwich"

When you heat up a piece of glass, two things happen:

It gets physically thicker (like a metal bridge expanding on a hot day).
The glass gets "denser" to light (the light has to work harder to travel through it, effectively slowing it down).

Both of these changes make the "sandwich" slightly taller from the light's perspective. Because the researchers' "light radar" is so sensitive, they can see the glass getting thicker and "slower" just by looking at how the light bounces back.

4. The Experiment: A Hot Bath

They put the glass slide in a pot of water and slowly heated it up, like making tea.

The Result: As the water got hotter, the glass expanded and changed its optical properties. The "light radar" saw the distance between the top and bottom of the glass grow.
The Math: They found a perfect straight line: for every 1 degree Celsius the temperature went up, the glass "grew" by about 12.4 nanometers.
The Analogy: It's like a thermometer where the mercury doesn't rise in a tube; instead, the glass itself stretches by a microscopic amount, and a super-precise camera counts the stretch.

5. The Computer "Crystal Ball"

The researchers didn't just guess; they built a computer simulation (a digital twin of their experiment).

They used math to predict exactly how the water would swirl and how the glass would heat up.
They compared their real-world measurements with the computer's predictions.
The Result: The computer and the real experiment agreed within 5%. This proved that their theory was solid and that the glass really was acting as a perfect thermometer.

6. Why This Matters

Why bother turning a cheap glass slide into a thermometer?

No Touching: You can measure the temperature of something delicate (like a tiny microchip or a living cell) without sticking a probe into it, which might break it or change its temperature.
Cheap and Easy: You don't need a million-dollar sensor. You just need a standard glass slide and this light setup.
Super Stable: They tested it by scanning the glass over and over, and the measurements were incredibly consistent (stable to within 10 nanometers).

The Big Picture

This paper is like discovering that a common rubber band can be used as a precision scale. By understanding exactly how the rubber band stretches when you pull it, you can weigh things very accurately.

Here, the "rubber band" is a piece of glass, and the "pull" is heat. The researchers showed us that with the right "light radar," a simple piece of glass can tell us exactly how hot it is, opening the door to measuring temperatures in places where traditional thermometers just can't go.

1. Problem Statement

Contactless and localized temperature measurement is critical for applications involving microfluidics, lab-on-a-chip systems, and semiconductor manufacturing, where invasive sensors can alter system properties or fail at micro/nanoscales. While various optical methods exist (e.g., infrared thermography, Raman spectroscopy), there is a need for high-sensitivity, spatially resolved, and cost-effective techniques capable of measuring temperature gradients within transparent solids without physical contact. Standard Optical Coherence Tomography (OCT) lacks the phase stability required for nanometer-scale Optical Path Difference (OPD) detection necessary for precise thermal sensing.

2. Methodology

A. Experimental Setup

System Configuration: The authors utilized a Phase-Sensitive Optical Coherence Tomography (PhS-OCT) system in a common-path spectral-domain configuration.
- Source: A white-light laser (NKT SuperK Extreme) with a spectral bandwidth restricted to 200 nm.
- Detection: An Ocean Optics HR4000 spectrometer.
- Sample: A standard 1-mm-thick soda-lime glass slide immersed in a distilled water thermal bath.
- Principle: The system treats the glass slide as a self-referencing interferometer. Interference occurs exclusively between reflections from the front and back surfaces of the slide, eliminating the need for a separate reference arm and enhancing phase stability.
Temperature Control: The bath was heated using a PID-controlled ceramic hot plate with a PT100 sensor for ground-truth temperature monitoring. The setup ensured thermal equilibrium before data acquisition.

B. Data Processing & Phase Retrieval

Maximum Amplitude Zone (MAZ) Method: Unlike traditional single-point phase retrieval, the authors developed a robust algorithm:
1. Perform a Fourier Transform on the interference signal.
2. Define a "Maximum Amplitude Zone" (50% of peak modulus) around the signal peak.
3. Calculate the phase at 33 points within this zone.
4. Compute the circular mean of these complex phase values.
Advantage: This multi-point averaging suppresses phase-wrapping artifacts and reduces noise, enabling OPD detection stability below 10 nm.

C. Theoretical Modeling

OPD-Temperature Relationship: The change in Optical Path Length ( $\Delta z$ $Δ z$ ) is modeled as a function of temperature change ( $\Delta T$ $Δ T$ ), combining two effects:
1. Thermal Expansion: Change in physical thickness ( $L$ ).
2. Thermo-optic Effect: Change in refractive index ( $n$ ).
Equation: $\Delta z \approx L(T_0) \left( \frac{dn}{dT} + \beta n(T_0) \right) \Delta T$ $Δ z \approx L (T_{0}) (\frac{d n}{d T} + β n (T_{0})) Δ T$ .
- Parameters used: $\beta = 8.3 \times 10^{-6}/^\circ\text{C}$ (volumetric expansion), $dn/dT \approx 0.9 \times 10^{-6}/^\circ\text{C}$ (estimated for 800 nm).
Computational Simulation: A 3D Finite Volume Method (FVM) simulation using OpenFOAM was performed to model heat transfer (convection and radiation) in the water bath. This validated that the PT100 sensor reading accurately represented the temperature at the glass slide's measurement point, accounting for Rayleigh-Bénard convection cells.

3. Key Contributions

Novel Sensor Concept: Demonstrated the use of a standard, low-cost commercial glass slide as a calibrated interferometric thermometer, eliminating the need for custom-fabricated sensors.
Enhanced Phase Retrieval Algorithm: Introduced a multi-point circular mean phase calculation within the MAZ, which effectively mitigates phase-wrapping ambiguities and improves measurement robustness compared to single-point methods.
Comprehensive Validation: Combined experimental data with a high-fidelity computational fluid dynamics (CFD) model to verify thermal homogeneity and validate the theoretical OPD-temperature correlation.
Uncertainty Quantification: Provided a rigorous uncertainty analysis, establishing confidence intervals for the temperature measurements.

4. Results

Sensitivity: The system achieved a linear correlation between OPD and temperature in the range of 20–52°C.
- Experimental Sensitivity: $12.4 \pm 1.9$ nm/°C.
- Theoretical Sensitivity: $\approx 13.5$ nm/°C (based on material coefficients).
- Agreement: The experimental and theoretical values showed an 8.5% agreement, validating the physical model.
Simulation Accuracy: The OpenFOAM thermal simulations matched experimental temperature profiles with a Mean Absolute Percentage Error (MAPE) of 4.97%, confirming the uniformity of the thermal bath.
Repeatability & Stability:
- Repeated lateral scans at constant temperature demonstrated sub-10 nm stability (specifically, standard deviation $s = 1.4$ nm).
- This level of precision supports future applications in spatially resolved thermal mapping.
Linearity: All measurement series (S1–S7) exhibited correlation coefficients ( $R^2$ ) exceeding 0.99.

5. Significance and Future Outlook

Cost-Effectiveness: By utilizing standard glass slides and a simplified common-path OCT setup, this method offers a low-cost alternative to complex thermal sensors.
Non-Invasive Sensing: The technique allows for internal temperature monitoring of transparent solids without altering the material's properties, crucial for microfluidics and biological tissues.
Applications: The method is applicable to industrial process monitoring, biomedical temperature mapping (e.g., retinal therapy, bone surgery), and the characterization of thermo-optic coefficients in new materials.
Future Work: The authors plan to extend this technique to 2D thermal gradient reconstruction and validate the approach across diverse glass compositions and materials.

In conclusion, this work successfully establishes PhS-OCT as a highly sensitive, reliable, and accessible tool for localized temperature sensing in transparent solids, bridging the gap between theoretical modeling and practical, low-cost implementation.