Endoscopic pyrometric temperature sensor

Sergio Vilches; Çağlar Ataman; Hans Zappe

doi:10.1364/OL.383337

Laser, radio frequency, and plasma surgical procedures involve heating of tissue, as either the main treatment mechanism or as an unwanted byproduct [1–6]. During such a procedure, the surgeon controls and monitors the treatment using a combination of heuristics and visual feedback. However, these methods become challenging during endoscopic or robotic surgery due to the reduced maneuverability and the impaired visual information. A number of different temperature measurement techniques have been recently developed to overcome this problem [5], predominantly using thermocouples or fiber Bragg gratings. These sensors require direct contact with the tissue and are thus prone to damage by the ablation source [7]. Furthermore, their measurement bandwidth is limited by the heat transport between the treated area of the tissue and the sensor, limiting their usefulness in pulsed treatments.

We present here a fiber-based, non-contact temperature sensor that is particularly suitable for integration into endoscopic/laparoscopic and robotic surgery tools. Pyrometric sensors estimate the temperature of an object by analyzing its emitted thermal radiation, providing a means for non-contact yet accurate measurements [8]. Commonly used for measuring body temperature through the ear canal [9–11], it has to date not been used in endoscopic applications due primarily to the difficulties in the transmission of the thermal radiation from the distal to the proximal end.

At body temperature or typical temperatures that arise during laser or plasma surgery, the tissue radiation peaks in the mid-IR (MIR) region. It is possible to use chalcogenide-based optical fibers designed to work in this wavelength range [6]; however, their high cost, sensitivity to liquids, and limited operating temperature range (up to 96°C [12]) restrict their use in disposable catheters or when a high-temperature process is involved. Fused silica [near-IR (NIR)] fibers excel in their mechanical, chemical, and thermal characteristics, but they have a limited MIR transmission: their transmission is limited by multi-phonon losses towards longer wavelengths [13]. Due to the low power available in this range, NIR pyrometry has been restricted mostly to the measurement of high temperatures (above 400°C) [4].

In this work, we discuss the design, implementation, and theoretical and experimental performance of an endoscopic temperature sensor with a noise-equivalent temperature difference (NETD) better than 1°C at body temperature. The sensor combines low-noise-detection electronics and mechanical modulation for lock-in detection for noise reduction and stable operation.

Figure 1 depicts the pyrometric remote temperature measurement scheme. At the distal end, the blackbody radiation emitted from the treated area is collected by a NIR fused silica fiber with a planar, polished facet (Ceramoptec WFGe, 360 µm core diameter, 3.1 m long, 0.37 NA). A collimation/focusing lens system (Thorlabs C028TME-D) and an extended range InGaAs detector (Hamamatsu G12183-205K, 0.5 mm diameter, temperature controller (TEC) cooled to $-30^\circ {\rm C}$, with a dark current of 60 nA), followed by a transimpedance amplifier (Femto LCA-20K-200M, $ 200\;{\rm MV}\;{{\rm A}^{ - 1}} $, 20 kHz bandwidth, $ 14\;{\rm fA}/ \sqrt {{\rm Hz}} $ NEP) are used for detection. In order minimize the influence of the photodiode thermal noise and drift, a digital lock-in detection system is used.

Pyrometric temperature sensors estimate the temperature of an object by quantifying its thermal radiation. The spectral power density of thermal radiation from an ideal body at temperature $ T $ is described by

(1)$${B_\lambda }(\lambda ,T) = \varepsilon (\lambda ,T)\frac{{2h{c^2}}}{{{\lambda ^5}}}\frac{1}{{{e^{\frac{{hc}}{{\lambda {k_{\rm B}}T}}}} - 1}},$$

where $ \varepsilon (\lambda ,T) $ is the emissivity of the object, $ h $ Planck’s constant, $ c $ the speed of light, and $ {k_{ B}} $ the Boltzmann constant [4]. For $ {T = 36^ \circ }{\rm C} $, the maximum irradiance is located in the MIR region at 9.4 µm and decays exponentially for shorter wavelengths.

The minimum measurable temperature of a pyrometry system is limited by the SNR at the detector, which is defined by the ratio of the total detected power and the noise floor of the detection electronics. The former of these is limited by two factors: the etendue of the fiber and the cumulative spectral response of the entire system.

Fig. 1. Simplified representation of the endoscopic temperature sensor. A multimode silica fiber collects the blackbody radiation from the treated area that covers its entire FoV. The collected light is modulated by a mechanical chopper for lock-in detection.

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The optical power that can be coupled from a diffuse radiation source into an optical fiber is defined by the etendue ($ G $) of the fiber, which is given by

(2)$$G = {A_{{\rm fiber}}}{\Omega _{{\rm fiber}}},$$

where $ {A_{\rm fiber}} $ is the area of the fiber core, and $ {\Omega _{\rm fiber}} $ is the collection solid angle given by

(3)$${\Omega _{\rm fiber}} = \pi {\rm NA}_{{\rm fiber}}^2 = \pi {(\sin {\theta _{{\rm max}}})^2},$$

assuming a collection efficiency of 1 until $ {\theta _{{\rm max}}} $ [14]. As long as the field of view of the fiber observes a uniform temperature distribution, the power coupled into the fiber will be independent of the angle, shape, or distance to the object, and can be calculated as the product of radiance and etendue:

(4)$${P_{{\rm opt}}}(\lambda ,T) = {B_\lambda }(\lambda ,T)G.$$

The total power arriving at the detector is determined by the transmission spectrum of all the components in the detection scheme and can be calculated as

(5)$${P_{{\rm det}}}(\lambda ,T) = {\eta _{{\rm fiber}}}(\lambda ){\eta _{{\rm optics}}}(\lambda ){\eta _{{\rm detector}}}(\lambda ){B_\lambda }(\lambda ,T)G,$$

where the $ \eta $ terms denote the respective power efficiencies of the system’s components. Based on the previous analysis, the available optical power at the detector is optimized by maximizing the diameter and numerical aperture of the collection fiber (both affecting quadratically the collected power). The diameter of the fiber, 360 µm, was optimized for use in flexible endoscopes with a minimum bending radius over 18 mm. The numerical aperture was maximized by choosing a fiber chemistry based on germanium-doped silica, with a numerical aperture of 0.37.

To minimize absorption losses, the lens system at the proximal side of the endoscope uses chalcogenide lenses with a total transmittance of 65% in the NIR–MIR spectrum. The transmitted power is ultimately limited by multi-phonon absorption in the fused silica fiber [13], and the only optimization possibility is shortening the length of the fiber. To ensure compatibility with a wide range of endoscopes and endoscopic surgery equipment, the length of the fiber is chosen as 3.1 m.

Figure 2 compares the spectral shape of an ideal blackbody radiator at 36°C with the relative sensitivity of the sensor system, obtained as the product of the optical transmissivity of all the optical components and the relative sensitivity of the photodetector. An extended range InGaAs cooled detector was chosen as optimal for this wavelength range.

Fig. 2. Spectral power distribution of an ideal blackbody radiator at 36°C (gray) and modeled collection efficiency of the proposed NIR pyrometry setup.

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The measured output signal voltage of the detector $ V(T) $ can be calculated by integrating $ {B_\lambda }(\lambda ,T) $ over the relevant spectrum:

(6)$$V(T) = \int_\lambda {P_{{\rm det}}}(\lambda ,T)R(\lambda ){A_{{\rm V}/{\rm A}}}{\rm d}\lambda ,$$

taking into account the responsivity $ R $ of the detector and the gain $ {A_{{\rm V}/{\rm A}}} $ of the transimpedance amplifier. Figure 3 compares the result of this calculated integral with measurement values acquired using a custom blackbody reference radiator composed of a ceramic heater coated with soot, temperature controlled using an embedded PT100 sensor, as the source.

Fig. 3. Output signal from the pyrometry system modeled after Eq. (6) (assuming $ \varepsilon = 1 $) compared with the experimental datapoints obtained through three consecutive calibration runs.

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Given the computational cost of the integral, it is common to model Eq. (6) with the Sakuma–Hattori equation, which provides a closed-form expression [15] as

(7)$$S(T) = \varepsilon \frac{C}{{\exp \left( {\frac{{{c_2}}}{{AT + B}}} \right) - 1}},$$

where $ \varepsilon $ is the surface emissivity, $ A,B $, and $ C $ are calibration constants, and $ {c_2} $ is the second radiation constant given by $ hc/{k_B} $. The object temperature can then be estimated by the inverse equation

(8)$$T = \frac{1}{\varepsilon } \left[\frac{{{c_2}}}{{A\ln \left( {\frac{C}{S} + 1} \right)}} - \frac{B}{A}\right].$$

The minimum measurable temperature of a pyrometer is limited by the noise floor. The fundamental noise component of a pyrometer originates from the shot noise of the measured signal. An incident power $ S $ on the photodiode induces a photocurrent:

{I_{{\rm signal}}} = \frac{{\mu e}}{{h \nu }}S,

where $\unicode{x00B5}$ is the quantum efficiency of the detector. This photocurrent exhibits a shot noise $ {\overline {{i^2}} _{{\rm signal}}} = 2\textit{eB}{I_{{\rm signal}}} $, where $ B $ is the bandwidth of the system. The background radiation emitted by the housing of the photodiode also induces a photocurrent and thus contributes to the total shot noise. Together with the dark current of the photodiode and the excess noise arising from amplification, the total detector noise can be described as

(9)$${\overline {{i^2}} _{{\rm total}}} = 2\textit{eB}({I_{{\rm signal}}} + {I_{{\rm background}}} + {I_{{\rm dark}}}) + {\overline {{i^2}} _{{\rm excess}}}.$$

For an implementation with a bandwidth of 10 Hz, the fundamental signal shot noise for an object at 36°C would account for an rms current noise of 20.6 fA. The background radiation can be estimated using Eqs. (5) and (7), setting the etendue value to the difference between the detector etendue (with an ${\rm NA} = 1$) and the fiber etendue, and assuming an ambient temperature of 25°C, resulting in 60.4 fA. The excess noise added by the transimpedance amplifier is 62.6 fA (extracted from the manufacturer’s values), and the total noise in the system is measured to be 331 fA. From these values, and using Eq. (9), we estimate the dark current of the photodiode to be the main noise contributor, with an amplitude of 325 fA. It can be concluded that the pyrometer performance is limited by the dark current of the photodiode, already optimized by minimizing the active volume of the active area of the photodiode [16] and lowering the temperature of the junction to $-30^\circ {\rm C}$.

Photodiodes and transimpedance amplifiers are prone to long-term fluctuations in their offset (drift), leading to the measurement signal $ S = {S_{{\rm fiber}}}({T_{{\rm object}}},t) + {S_{{\rm offset}}}(t) $. To control drift, a lock-in detection scheme is implemented using a chopper wheel, as illustrated in Fig. 1. The optical signal from the collection fiber is blocked by a chopper wheel, which however also has a finite temperature when the signal is blocked, leading to the signal $ S = {S_{{\rm chopper}}}({T_{{\rm chopper}}}) + {S_{{\rm offset}}}(t) $. By alternatively blocking the emission of the fiber reaching the photodiode, the AC signal measured then has a peak-to-peak amplitude of

(10)$${S_{{\rm pp}}} = {S_{{\rm fiber}}}({T_{{\rm object}}}) - {S_{{\rm chopper}}}({T_{{\rm chopper}}})$$

for chopper wheel temperature $ {T_{\rm chopper}} $, in which $ {S_{{\rm offset}}}(t) $ is cancelled out. For the practical implementation of this algorithm, it is necessary to estimate the coefficients of the Sakuma–Hattori transfer functions $ {S_{{\rm fiber}}}({T_{{\rm object}}}) $ and $ S = {S_{{\rm chopper}}}({T_{{\rm chopper}}}) $, and to continuously monitor the temperature of the chopper wheel. In the current setup, the chopper temperature is measured using a Texas Instruments LM35 temperature sensor placed 5 mm away from the chopper.

The lock-in signal processing is implemented digitally using a digital acquisition system (DAQ) with 1 MSPS, 16-bit (NI USB 6251), and a mechanical chopper wheel modulating at 2.2 kHz. The signal from the photodiode is demodulated using a reference signal from the chopper controller and then low-pass filtered to 10 Hz. Faster tissue dynamics can be observed by increasing the chopping frequency and the low-pass filter corner frequency at the cost of an increased measurement noise. As an example, 1 kHz bandwidth would increase the minimum measurable temperature (defined as 1°C NETD) to 75°C.

The effectiveness of lock-in detection in the control of drift can be observed in Fig. 4, where the measured temperature of the reference blackbody radiator does not drift more than the noise level for 1 h.

Fig. 4. Long-term evolution of the measured temperature (red) through 1 h for different object temperatures (36°C, 100°C, and 175°C), compared with the reference temperature (black). The zoomed-in plots show fluctuations arising from the temperature controller at high temperatures.

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Fig. 5. Comparison of modeled and measured noise-equivalent temperature difference (NETD) versus object temperature for the implemented pyrometer.

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The noise performance of a pyrometer is conventionally expressed as its NETD, defined as the temperature difference that would produce a signal equal to the sensor’s temporal noise [17]. The influence of the photodiode noise is more relevant when measuring objects at lower temperatures and can be calculated by using the first derivative of Eq. (8):

(11)$${\left.\frac{{\delta T}}{{\delta S}} \right|_T} = {\left[ {{{\left[ {S(T)} \right]}^2}\frac{{A{c_2}}}{{C{{\left( {AT + B} \right)}^2}}}\exp \left( {\frac{{{c_2}}}{{AT + B}}} \right)} \right]^{ - 1}}.$$

Using this equation, it is possible to translate the fixed intensity noise calculated in Eq. (9) to the NETD. The resulting model is plotted in Fig. 5, estimating an rms temperature noise smaller than 1°C for objects above 30°C, and decreasing exponentially towards higher temperatures. This model was tested against empirical data, overlaid in Fig. 5. It can be observed that the expected exponential decrease of noise is followed for low temperatures, but is eventually dominated by the fluctuations in the temperature of the reference blackbody source at higher temperatures. These fluctuations are induced by the temperature controller and can be clearly observed in Fig. 4 (top right plot).

The performance of the pyrometry setup was tested during a thermal hyperthermia procedure performed on ex vivo swine stomach. An LED source (360 nm, 1000 mW) was focused on a $5 \times 5\; {\rm mm}$ spot in the mucosa of the excised stomach. A catheter with the measurement fiber was placed in the vicinity of the focus spot, covering the complete field of view of the fiber. From the top, a thermal camera (FLIR ETS320) recorded the average temperature in the focus spot. The LED was alternatively turned on and off, inducing local heating. The resulting temperature profiles, acquired at 10 Hz, are plotted in Fig. 6.

Fig. 6. Temperature evolution of ex vivo tissue heated by a high-power LED, measured by the proposed fiber sensor and compared with a commercial thermal camera.

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The precision of the measurement observed in Fig. 6 agrees with the theoretical calculations and serves as a worst-case-scenario SNR test, as the temperatures involved are even below body temperature. On the other hand, this experiment represents an idealized medical procedure, free of body fluids or particles that might occlude the optical path and thus affect the collected power. The extent to which these external influences affect the measurement should be tested for particular medical procedures.

We have demonstrated a non-contact, high-speed, remote temperature sensor, overcoming the limitations of silica-fiber pyrometry with a novel combination of low-noise electronics and a robust sensor scheme. This efficient detection scheme enables for the first time endoscopic, contactless measurement of temperatures down to 30°C using a fiber of 360 µm core diameter and 3.1 m length. Due to the biocompatibility, robustness, and low price of fused silica fibers, this sensor opens the possibility of closed-loop temperature control of thermal surgery using an embedded, disposable catheter.

Funding

Bundesministerium für Bildung und Forschung (13N14343).

Disclosures

No conflicts of interest, financial or otherwise, are declared by the authors.

REFERENCES

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Endoscopic pyrometric temperature sensor

Abstract

Funding

Disclosures

REFERENCES

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Optics Letters