Simultaneous measurement of near-water-film air temperature and humidity fields based on dual-wavelength digital holographic interferometry

Mengmeng Zhang; Jingnan Liu; Jiazhen Dou; Jiwei Zhang; Lixin Zhang; Jianglei Di; Jianglei Di; Jianglei Di; Jianlin Zhao; Jianlin Zhao

doi:10.1364/OE.457640

1. Introduction

Evaporation is a common phenomenon that accompanies heat and mass transfer between liquid and gas. The evaporation of water plays an important role in many application fields, such as spray cooling, global circulation of water vapor, natural draft cooling tower for waste heat discharging in electric power plant, and so on. From a macro point of view, increasing the relative flow rate and evaporation area is conducive to enhancing the evaporation effect. A lot of works have been done to explore the mechanism of evaporation, and establish the relationship between various physical quantities and heat and mass transfer in the evaporation process [1–3]. Yu and Song et al. systematically studied the falling-film flowing wave on vertical plates of the nuclear power plant containment cooling technology, and obtained the flowing mode of multiple wave forms [4,5]. Li et al. studied the reverse flow of air and water film and found a critical velocity. The water film would be greatly affected if air velocity is greater than the critical velocity [6]. Although there have been many studies on water drop and water film systems, the microscopic processes have not been deeply understood yet, such as the influence of the micro-distribution and the relative flow between water and air on the temperature and humidity distribution.

In order to study the evaporation phenomenon in depth, one of the most important prerequisites is accurate measurement and characterization of air temperature and humidity distributions. Traditional approaches for air temperature measurement include liquid thermometer, thermocouple, thermistor, radiation temperature measurement based on black body radiation principle, bimetallic sheet, pyrometer, etc [7,8]. For air humidity measurement, the approaches include double pressure or double temperature method, split flow method, saturated salt method, dry and wet bulb method, dew point method and humidity ratio absorption method, impedance method, etc [9,10]. However, most of the methods above require close contact between the object and measuring elements such as thermocouples, which are invasive and non-full-field measurement methods. Although the radiation measurement technique is a non-contact method, it’s hard to achieve high accuracy because of the surface emissivity of the object. Therefore, for the measurement of air temperature and humidity fields near the air-liquid interface, the above methods are nonuniversal and inapplicable.

The most obvious effect caused by the change of temperature and humidity fields is the change of air refractive index n. This results in a change in the optical path of the laser beam passing through the air. In this case, digital holographic interferometry (DHI), as one of the most typical quantitative phase measurement techniques, has been demonstrated to be a noncontact and nondestructive method in temperature field measurement. In DHI, the phase and amplitude information of the object field is numerically reconstructed from the hologram recorded by using a CCD or CMOS [11]. As it’s convenience, non-contact, real-time and high-sensitivity, DHI has become a powerful tool in the investigation of the dynamic characteristic of the physical processes, such as cell-substrate adhesion [12], thermal effect in laser pumped silicon [13], combustion process [14], liquid phase diffusion [15] and Rayleigh-Benard convection [16], and so on.

Due to the high resolution and high precision of DHI, as early as 2002, Zhao et al. studied the feasibility of DHI in the measurement of three-dimensional temperature distribution [17], and then used DHI to visually and quantitatively investigate the heat dissipation process of plate-fin heat sinks [18]. Later on, some other teams also conducted research on temperature field measurement with DHI [19–21]. The physical model of DHI applied to gaseous temperature field measurement are based on Gladston–Dale or Lorentz-Lorenz equation, where the impact of humidity is not involved. When the air temperature and humidity fields both change at the same time, the temperature is affected by two processes: the heat conducting caused by the momentum exchange of air molecules and the heat transporting caused by the diffusion of water molecules, whose temperature is different from the air’s. The humidity is also affected by two processes: the change of water vapor concentration caused by the diffusion of water molecules and the change of the local saturated vapor pressure caused by the temperature change. Those four processes are coupled with each other, so that the temperature and humidity of the air is difficult to be accurately and simultaneously measured with traditional methods. Because water vapor in air has a dispersion effect, different temperature and humidity will produce different optical path differences for light with different wavelengths. Hence, here we present a dual-wavelength DHI to decouple the temperature-humidity-coupling field. By applying spatial filtering in the holographic reconstruction process, the phase changes of two wavelengths are obtained. Then based on Edlen equation, the relationship between temperature, humidity and phase changes can be derived. According to this relationship, the temperature and humidity distributions will be solved simultaneously. This method was verified with a falling water film model (FWF model) [22] and its stability was also tested experimentally. The FWF model is able to generate various convection situations between water film and flowing air. The measurement results are instructive for the study of water film evaporation.

2. Theory

2.1 Dual-wavelength DHI

In dual-wavelength DHI, assuming that O₁ and O₂ are the complex amplitudes of two common-path object beams with wavelengths of λ₁ and λ₂ and passing through the air field with certain temperature and humidity distributions, respectively, and R₁ and R₂ are the complex amplitudes of corresponding reference beams with different spatial angles relative to the object beams. The intensity recorded by the camera can be expressed as [23]

(1)$$\begin{array}{c} I({x,y} )= {|{{O_1}({x,y} )} |^2} + {|{{O_2}({x,y} )} |^2} + {|{{R_1}({x,y} )} |^2} + {|{{R_2}({x,y} )} |^2} + \\ {O_1}({x,y} )R_1^\ast ({x,y} )+ O_1^\ast ({x,y} ){R_1}({x,y} )+ \\ {O_2}({x,y} )R_2^\ast ({x,y} )+ O_2^\ast ({x,y} ){R_2}({x,y} ), \end{array}$$

where the first four terms are zero order components, and the last four terms carry the object wavefronts of two wavelengths and their conjugations, respectively. Appling spectrum filtering for the spectral components separately [24], the complex amplitude of the two object beams O₁(x, y) and O₂(x, y) can be numerically reconstructed.

In order to eliminate the influence of the wavefront phase distribution of the reference waves, double-exposure method is used. By recording two holograms in two different states, the phase changes Δφ_i(x,y) between two reconstructed object waves of the two states can be calculated as

(2)$$\Delta {\varphi _i}({x,y} )= \arctan \frac{{{O_i}({x,y} )}}{{{O_{ref,i}}({x,y} )}},i = 1,2,$$

where O_ref,i(x,y) and O_i(x,y) are the complex amplitude of the object beam in initial state for reference and in final state to be measured, respectively.

2.2 Modified Edlen equation

The relationship between the phases and the refractive index changes of air induced by temperature and humidity changes can be derived from the Edlen equations revised by Cheng et. al in 2017 [25]. And then the relationship between the refractive indices of the air and the temperature, the partial pressure of water vapor, the air pressure, the concentration of CO₂ and the wavelength of light can be expressed as

(3)$${n_s} = \left( {{a_1} + \frac{{{a_2}}}{{{a_3} - {\sigma^2}}} + \frac{{{a_4}}}{{{a_5} - {\sigma^2}}}} \right) \times {10^{ - 8}} + 1,$$

(4)$${n_x} = ({{n_s} - 1} )[{1 + 0.5327({x - 0.0004} )} ]+ 1,$$

(5)$${n_{tp}} = \frac{{p({{n_x} - 1} )}}{{{b_1}}} \times \frac{{1 + {{10}^{ - 8}}({{b_2} - {b_3}t} )p}}{{1 + {b_4}t}} + 1,$$

(6)$${n_{tpf}} = {n_{tp}} - f({{c_2} - {c_3}{\sigma^2}} )\times {10^{ - 10}},$$

where σ[µm^-1] is the wave number, n_s is the refractive index of the dry air consisting with 78.09% of N₂, 20.92% of O₂ and 0.93% of Ar at 15°C, 101.325kPa, x is the concentration of CO₂ and is set to 0.0004 in the experiment, n_x is the refractive index of the above dry air when the concentration of CO₂ is x, t is the air temperature, n_tp is the air refractive index when CO₂ concentration is x and temperature is t, n_tpf is the air refractive index when CO₂ concentration is x, temperature is t, and water vapor partial pressure is f, and a_i, b_i, c_i are experimental constants shown in Table 1.

Table 1. Values of experimental constants [25]

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Based on Eqs. (3)–(6), the relationship between phase change and the temperature and humidity changes can be established as

(7)$$\Delta {\varphi _i} = [{{\varphi_t}({{t_0} + \Delta t,{\lambda_i}} )- {\varphi_t}({{t_0},{\lambda_i}} )} ]+ [{{\varphi_d}({{d_0} + \Delta d,{\lambda_i}} )- {\varphi_d}({{d_0},{\lambda_i}} )} ],i = 1,2,$$

where Δt and Δd are the temperature and humidity change, t₀ and d₀ are the initial values of temperature and humidity, respectively, Δφ_i is the phase change of object beam caused by temperature and humidity changes of every wavelength, and

(8)$${\varphi _t}({t,\lambda } )= \frac{{2\mathrm{\pi }L}}{\lambda } \times \frac{{p({{n_x} - 1} )}}{{{b_1}}} \times \frac{{1 + {{10}^{ - 8}}({{b_2} - {b_3}t} )p}}{{1 + {b_4}t}},$$

(9)$${\varphi _d}({d,\lambda } )={-} \frac{{2\mathrm{\pi }L}}{\lambda } \times \frac{{dp}}{{d + {c_1}}}({{c_2} - {c_3}{\sigma^2}} )\times {10^{ - 10}},$$

where L is the length of the measured air sample along the optical axis.

The detailed deriving of Eqs. (7)–(9) can be found in Section 1 of Supplement 1. For certain Δφ_1,2, Δt and Δd can be solved uniquely. The only parameters that cannot be measured with holography are the initial temperature t₀ and humidity d₀. Thus, calibration with temperature and humidity sensors or other auxiliary devices are required.

3. Experimental setup

Figure 1 shows the dual-wavelength DHI setup for measuring temperature and humidity fields of the near-water-film air. The diagram shown in Fig. 1(a) is composed of a dual-wavelength off-axis Mach-Zehnder interferometer.

Fig. 1. Dual-wavelength DHI setup for measuring temperature and humidity fields. (a) Diagram of the dual-wavelength DHI. CMOS: complementary metal oxide semiconductor; L_1-6: lenses; BS_1-2: beam splitters; M: mirror; P_1-3: polarizers; BE_1-3: beam expanders; FC_1-3: fiber couplers; FWF model: falling-water-film (FWF) model; (b) front view of the falling-water-film model. (c) Detailed view of how object beam passes FWF model.

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The two common-path beams out of laser₁ (CNILASER, MSL-FN-532-200 mW, 532 nm, λ₁) and laser₂ (CNILASER, MSL-FN-671-200 mW, 671 nm, λ₂) are split into object and reference beams by fiber coupler FC₁ and FC₃, respectively. The two object beams go through fiber coupler FC₂ to form the synthetic object beam. BE₃ and L₆ (Φ100 mm) form a reverse telescope system for beam expansion and collimation. L₁ and L₅ (Φ100 mm) form a telescope system to match the beam size to CMOS target (Baumer, LXG-200M, 5120 × 3840, pixel size 6.4 µm).

The synthetic object beam horizontally illuminates the FWF model and then projects onto the CMOS camera after passing though the telescope system L₁ and L₅. The two reference beams incident on the camera with different off-axis angles relative to the object beam. The off-axis angles can be adjusted separately by beam splitter BS₁ and reflecting mirror M. Three polarizers, P₁, P₂, P₃, are inserted into the reference and object beams to adjust the fringe contrasts of the hologram of every wavelength. The FWF model consists of copper plate, water inlet, inlet buffer, water outlet and walls. The copper plate is set in the middle of the object beam and is adjusted to be strictly parallel to the object beam to minimize the influence of the edge diffraction of the copper plate. One side of the copper plate is covered with a water film while the other side is kept dry. Two flat glasses are arranged at the front and end of the model to isolate the water vapor transmission on both sides of the copper plate. Four thermocouples, TC₁ to TC₄, and two HDC2080 temperature and humidity sensors, TWS₁ and TWS₂, are set in the FWF model for calibration and comparison.

The FWF model consists of an airflow rate control system, a water flow control system, a group of air temperature, humidity and pressure sensors, and a FWF evaporation device. The air speed control system consists of an axial fan, a 3D printed iris-type adjustable air valve, a DC power supply, etc. The air speed control system is connected to the top of the model with soft bellows to control the airflow in the model. The water flow control system is mainly composed of a constant temperature water tank and several water pipes, pumps, valves, etc. The constant temperature water tank is used to control the temperature of the water film precisely and the pumps and valves are used to control the flow rate. The sensors are made by HDC2080 and BMP280 driven by stm32 microcontrollers. Those sensors, together with thermocouples, are arranged throughout the model to collect data at the locations marked in Fig. 1(b). Those data are collected and saved synchronously with the holograms.

The FWF model is divided into two symmetrical tunnels by a copper plate: the evaporating tunnel and the reference tunnel. The water from the water tank flows across the model and forms a thin water film on the evaporating tunnel side of the copper plate. A single sheet of gauze is covered on the copper plate surface so that the water film can spread evenly. In the meantime, the axial fan provides constant airflow from bottom to up. Under such a condition, in the evaporating tunnel, the water film transfers both mass and heat with air while in the reference tunnel, only heat transferring exists, forming a contrast to the evaporating tunnel.

For holographic measurement, the uniformity of air temperature and humidity distributions is very important for accuracy. In the FWF model, the copper plate and water pipes for water film producing, and the air inlets, air outlets, and air ducts for airflow controlling are made completely symmetrical. Besides, considering that there is a boundary layer in airflow, the length of the model is made to be 18 cm, which is much larger than the thickness of boundary layer, to eliminate the influence of the inhomogeneity of temperature and humidity distribution on the measurement.

4. Experiment results and discussions

There are three steps to solve the distributions of air temperature and humidity: reconstructing the phase distributions of the object beams of λ₁ and λ₂, solving Eq. (4), and applying calibration.

4.1 Reconstruction of phase distributions of object fields

Figure 2 shows one of the recorded holograms of the FWF model. The middle vertical shadow is the projection of the copper plate. The areas of the evaporating tunnel and reference tunnel are unconnected, so each of the holograms is separated into two striped segments of the shapes of evaporating tunnel and reference tunnel, marked with blue and red dashed lines, respectively. Reconstruction is applied to every segments separately. Figure 3 shows the reconstructed phase distributions of each segment and how they are pieced together. The coordinate (ξ, η) is the discreate pixel position in the phase image, the relation between whom and the real coordinate system in FWF model can be found in Section 2 of Supplement 1.

Fig. 2. Recorded hologram and its spatial spectrum in the experiment. (a) Hologram; (b) spatial spectrum of (a). First order frequency spectrum of λ₁ and λ₂ are marked with green circle and red circle, respectively.

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Fig. 3. Reconstructed wrapped phase (35 °C, 2.95 m/s). (a) Wrapped phase of λ₁; (b) wrapped phase of λ₂; (c) cross sections of the wrapped phases of λ₁ and λ₂ at the positions marked in (a, b).

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In Fig. 3, there are noticeable phase noise near the edge of the copper plate due to diffraction effect. However, this is the place where the heat source for calibration is and the phase gradient is rather large. Inaccurate phase unwrapping in this region results in incorrect reconstruction of the temperature and humidity fields.

What’s more, the equations to solve temperature and humidity based on phase changes are ill-conditioned. Typical condition numbers are around 20. Thus, small perturbations in the coefficients or phases will cause a huge error in the results.

To solve this problem, we propose the particle swarm optimization (PSO) based edge enhancement method. The basic idea is to fit out the relationship between phase values and spatial coordinates, and then filter out the outliers with the fitted value. The edge enhancement method is described as an optimization problem

(11)$$\left\{ \begin{array}{l} \min \frac{1}{N}\sum {{{({{\varphi^\ast } - \varphi } )}^2}} ,\\ s.t.\sum\limits_{i = 1}^n {{a_i} = 1,\sum\limits_{i = 1}^2 {{w_i} = 1} } , \end{array} \right.$$

where N is the total pixel number of phase image, φ* is the fitted phase, and a_i and w_i are fitting coefficients and weights, respectively. Detailed demonstration can be found in Section 3 of Supplement 1. One set of fitting coefficients, weights and standard deviation (SD) is shown in Table 2.

Table 2. PSO fitting coefficients.

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Here, φ_i_{, evap} and φ_i_{, ref} represent the evaporating and reference segments of the phase maps of λ_i, respectively.

The relationships between fitted φ* and X are plotted in Fig. 4. The outliers are clearly filtered out and the enhanced phase distributions are shown in Fig. 5.

Fig. 4. Plots of PSO fitting results (35 °C, 2.95 m/s). (a), (b) Evaporating tunnel for wavelengths of 532 nm and 671 nm; (c), (d) reference tunnel for wavelengths of 532 nm and 671 nm.

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Fig. 5. Comparison of the unwrapped phase with and without PSO edge enhancement (35 °C, 2.95 m/s). (a), (b) Unwrapped phase without and with PSO edge enhancement of λ₁; (c), (d) unwrapped phase without and with PSO edge enhancement of λ₂; (e-h) detail of above images.

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4.2 Calculation of temperature and humidity

Next step is to solve the nonlinear Eqs. (7)–(9). Two approaches are used: the linearization and substitution. The linearization approach takes the first-order approximation to make the equation set linear, while the substitution approach uses variables to represent the nonlinear items of temperature t and humidity d. Error analysis shows that the linearization method is suitable for obtaining t, while the substitution method is suitable for obtaining d. Detailed demonstration of the two methods can be found in Section 4 of Supplement 1.

The solution for Eqs. (7)–(9) only contains the changes of temperature and humidity, Δt(x,y) and Δd(x,y). In order to obtain the real temperature and humidity distributions, calibration is necessary. The monitor points marked in Fig. 1(b) give the initial temperature and humidity values t₀ and d₀. The temperature and humidity distributions can be easily calculated as

(12)$$t({x,y} )= {t_0} + \Delta t({x,y} ),$$

(13)$$d({x,y} )= {d_0} + \Delta d({x,y} ).$$

However, as shown in Tab. S1, even with the best approach, there are still 16.26% error for t and 11.94% error for d. Such error can also be minimized with PSO.

(14)$$\left\{ \begin{array}{l} \min \sum {[{{{({{t^\ast } - t} )}^2} + {{({{d^\ast } - d} )}^2}} ],} \\ s.t.\;\mathrm{\delta }({{n_s}} )\mathrm{\leqslant }3 \times {10^{ - 9}},\mathrm{\delta }(p )\mathrm{\leqslant }600\;\textrm{Pa},\mathrm{\delta }(t )\mathrm{\leqslant }0.1{\;^\textrm{o}}\textrm{C},\delta (d )\mathrm{\leqslant }2\%. \end{array} \right.$$

where t* and d* are sensor values, and the constraints come from the measuring instruments and research [25].

Another factor that is able to cause measurement error is the stability of the optical set. Detailed stability analysis can be found in Section 5 of Supplement 1.

Finally, the distributions of temperature and humidity with minimum error is reconstructed. Figure 6 shows a group of measurement results for temperature and humidity. The relationship between heat and mass transfer, water temperature and air speed are clearly shown.

Fig. 6. Plot of temperature and humidity reconstruction results (35 °C, 2.95 m/s). (a) Temperature distribution; (b) humidity distribution; (c) cross sections of the temperature and humidity distributions at the positions marked in (a, b); (d) plots of cross sections of the temperature distributions under different working conditions; (e) plots of Cross sections of the humidity distributions under different working conditions.

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In the experiment, part of the temperature and humidity sensors were used to determine the measurement accuracy. By comparing the reconstructed temperature and humidity with the sensor values, the measurement error can be obtained, as is shown in Table 3.

Table 3. Measurement error

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The measurement errors of the temperature, humidity and humidity ratio are 3.41%, 0.64% and 3.37%, respectively. The precision of thermocouples and humidity sensors used for comparison are 0.1 °C and 2%, respectively.

The results show that near the water film, the temperature and humidity are both high, but in the reference tunnel, the humidity drops. That is because the humidity ratio in the reference tunnel remains constant while the temperature near the copper plate increases, resulting in an increase in saturated vapor pressure. The temperatures on the two sides of the copper plate are roughly equal. Near the water film, the air humidity approaches 100% and water vapor is close to saturation while it drops sharply in the air away from the water film. The temperature distribution is similar to that of humidity. However, in the reference tunnel, the regularity is different. Near the dry side of the copper plate the humidity ratio remains constant, so air humidity drops due to temperature and saturated vapor pressure increment. Far from the copper plate, the temperature is lower than that in the evaporating tunnel. Thus, the existence of evaporation would cause the temperature to change more smoothly, and it also accelerates the heating of the air in the evaporating tunnel.

It is noticeable that the temperature and humidity tend to rise near the right edge of the evaporating tunnel. A possible reason is that there is a thin boundary layer near the wall. The closer to the wall, the slower the air would be. After the water vapor with a higher temperature diffuses to the wall, it will be bound to the wall and cannot discharge quickly. Therefore, the water vapor near the wall accumulates until the equilibrium of diffusion and confinement is reached, so the temperature and humidity there are higher.

Comparing the cross sections under different conditions, increasing the temperature of the heat source will cause significant influence on the temperature field, but the humidity field is almost independent of water film temperature. Airflow only causes small changes to the temperature and humidity fields. Comparing the temperature distributions in the evaporating tunnel and reference tunnel, conclusion can be drawn that evaporation promotes the diffusion of heat and causes the temperature distribution more even. A possible explanation is when water molecules evaporate into the air, they increase the heat in the air directly, which is more efficient than pure heat convection.

5. Conclusions

In this paper, through decoupling multiple quantities using the dispersion effect, the air refractive index equation has been derived based on Edlen equations to reconstruct the air temperature and humidity distributions with two different wavelengths. The full-field air temperature and humidity distributions in the falling water film model have been measured simultaneously by using dual-wavelength digital holographic interferometry. Several conclusions are listed below: (1) The method of combining Edlen equations and DHI is able to simultaneously measure the air temperature and humidity distributions in the FWF model. (2) The proposed data enhancement methods such as PSO edge enhancement and error analysis of non-linear equation sets can be used to increase the measurement accuracy of DHI, and the precision reaches 3.41% for temperature measurements and 0.64% for humidity measurements. (3) The results shows that evaporation promotes the diffusion of heat and makes the temperature distribution more even. (4) The measure results are accurate but not precise enough. For further improvement, higher-precision-and-resolution CCDs or CMOSs and weaker coherent laser sources can be considered.

Funding

National Natural Science Foundation of China (61927810, 62075183, 62005219); Fundamental Research Funds for the Central Universities (310202011qd004).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Name	Value	Name	Value	Name	Value	Name	Value
a₁	8091.37	a₄	15518	b₂	0.5953
a₂	2333983	a₅	38.9	b₃	0.009876	c₂	3.9969
a₃	130	b₁	93214.6	b₄	0.003661	c₃	0.059

Segment	Coefficients					Weights		SD
Segment	a₀	a₁	a₂	a₃	a₄	w₁	w₂	s
φ_1,_evap	28.6822	-0.6704	0.4092	0.2430	-0.2195	-0.2138	1.2138	0.0456
φ_2, _evap	80.7920	-4.4606	2.8391	1.1040	-1.3776	-0.2150	1.2150	0.0376
φ_1,_ref	54.7242	0.6504	0.6261	-0.1983	-0.5802	-0.0325	1.0325	0.1640
φ_2,_ref	59.8638	-1.0448	-0.9013	0.5814	0.9255	-0.0483	1.0483	0.0621

	Evaporating tunnel		Reference tunnel
	Temperature	Humidity	Temperature	Humidity Ratio
Unit	°C	%	°C	kg/kg
Measured value	34.87	100.61	34.79	18.20
Monitor value	33.72	100.00	34.71	18.84
Error	1.15	0.61	0.08	0.64
Relative error	3.41%	0.61%	0.22%	-3.37%

Name	Value	Name	Value	Name	Value	Name	Value
a₁	8091.37	a₄	15518	b₂	0.5953
a₂	2333983	a₅	38.9	b₃	0.009876	c₂	3.9969
a₃	130	b₁	93214.6	b₄	0.003661	c₃	0.059

Segment	Coefficients					Weights		SD
Segment	a₀	a₁	a₂	a₃	a₄	w₁	w₂	s
φ_1,_evap	28.6822	-0.6704	0.4092	0.2430	-0.2195	-0.2138	1.2138	0.0456
φ_2, _evap	80.7920	-4.4606	2.8391	1.1040	-1.3776	-0.2150	1.2150	0.0376
φ_1,_ref	54.7242	0.6504	0.6261	-0.1983	-0.5802	-0.0325	1.0325	0.1640
φ_2,_ref	59.8638	-1.0448	-0.9013	0.5814	0.9255	-0.0483	1.0483	0.0621

Simultaneous measurement of near-water-film air temperature and humidity fields based on dual-wavelength digital holographic interferometry

Abstract

1. Introduction

2. Theory

2.1 Dual-wavelength DHI

2.2 Modified Edlen equation

3. Experimental setup

4. Experiment results and discussions

4.1 Reconstruction of phase distributions of object fields

4.2 Calculation of temperature and humidity

5. Conclusions

Funding

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (6)

Tables (3)

Equations (13)

Optics Express