Small displacement measurements based on an angular-deviation ...

Small displacement measurements based on an angular-deviation amplifier and interferometric phase detection Ming-Hung Chiu,* Wei-Chou Chen, and Chen-Tai Tan Department of Electro-Optical Engineering, National Formosa University, No. 64, Wunhua Road, Huwei, Yunlin 632, Taiwan *Corresponding author: [email protected] Received 27 November 2014; revised 2 March 2015; accepted 3 March 2015; posted 3 March 2015 (Doc. ID 228665); published 27 March 2015

We propose a method for small displacement measurement based on the angle deviation to phase change transformation. The phase change of common-path heterodyne interferometry due to the angle deviation of incidence of a light at interfaces caused by the displacement is detected by a lock-in amplifier. To obtain more accurate results we used an angular amplifier to increase the angle deviation and utilized a surface plasmon resonance (SPR) sensor to enhance the performance of phase detection. When a translator moves one of two face-to-face plane mirrors at an end and then rotates it a small angle, a light is incident onto the mirrors and reflected N times. The outgoing light is also deflected N times of the angle and incident into a SPR sensor. Thus the phase shift due to the angle deviation is amplified N times. The accumulated phase shift is proportional to the amplified angle deviation and displacement. Therefore, the phase change is obtained and the displacement is measured. The amount of movement required can be as low as 0.13 μm without an SPR sensor or 0.08 μm with an SPR sensor. The maximum measurement range can reach 1000 μm. © 2015 Optical Society of America OCIS codes: (120.5050) Phase measurement; (120.3180) Interferometry; (040.2840) Heterodyne; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/AO.54.002885

1. Introduction

Heterodyne interferometry, particularly the configuration of the Michelson interferometer, is an important technology for small displacement measurements. Though periodic nonlinearity error can occur, its measurement precision is still within 1 nm [1–3]. Most heterodyne light can be provided by a laser itself, such as the Zeeman laser [1,2], or can be modulated by an acousto-optic modulator [4] or an electro-optic modulator [5–7]. Its beat frequency range is from kHz to MHz, and its phase resolution can be up to 0.01°. In addition to using the Michelson interferometer structure, the structure of common-path heterodyne

1559-128X/15/102885-06$15.00/0 © 2015 Optical Society of America

interferometry (CPHI) can be another viable option [8]. By using heterodyne lights, two polarizations (the s- and p-polarizations) that are orthogonal and have a frequency difference, travel on the same route. The optical parameters or some physical quantities of the test sample can be found with the difference of phase shift caused by the angle change of incidence such as the index of refraction [8,9], small angle [10,11], small displacement [12], etc. Therefore, this study uses the method of angular deviation by displacement in which the test beam produces a phase difference between the s- and p-polarizations. With an analyzer getting the interference in the direction of its transmission axis, the interference signal obtained is transformed into an electrical signal by a photodetector. It is ultimately connected with a lock-in amplifier or phase meter to compare it with the reference signal to analyze the phase 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS

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difference that occurred. This resulting phase difference is in direct proportion to angle deviation and displacement. For example, the multiple totalinternal reflection (TIR) angle deviation method [12] is used to measure a small displacement. The heterodyne beam focuses on the surface to be measured through a lens. When the surface to be measured makes displacement and defocuses, the reflection beam is changed into divergent light or convergent light. Assuming multiple TIRs in the prism because the angle of incidence on both sides of the beam varies, the phase shift difference between two edges of the beam is changed. In other words, a phase difference exists between two edge lights, and the displacement can be calculated by this phase difference. Although the method has a submicron resolution, the measurable range is only within 1 μm because of its nonlinearity. A surface plasmon resonance (SPR) sensor can also be used as angle sensor because it has a sharp phase change when at the resonant angle. The sensor can then be combined with the angle deviation method to measure small displacements [13,14]. Its resolution of displacement measurement can be as small as 1 nm but the measurable range is limited by the NA value and within several micrometers. Furthermore, in non-CPHI methods a grating can be added to make a small displacement measurement [15,16]. After the heterodyne light beam passes through said grating, overlaps the diffraction light, and interferes, its phase variation is also in direct proportion to displacement. The method can measure three degrees-of-freedom displacement in real time [16]. Their standard deviation of displacement measurement is about 3 nm. In 2012, Lee et al. [17] proposed using heterodyne speckle pattern interferometry to measure in-plane small displacement, which can achieve a resolution ratio as high as 5 nm. Although the non-CPHI methods have several nanometers resolution, the structures and environment must be under control to maintain their highprecision measurement results. If in a free space the disturbances, such as vibration, will result in larger errors because of phase jump, which may be larger than 2π in a random manner. This paper proposes measuring small displacement with CPHI, an angular amplifier, and an SPR sensor for at least larger than 100 μm measurement range with decade nanometer resolution. Because the range is the common size range of high-precision products, it is difficult to measure accurately. Another reason for the proposed method is that the measurement can be done on-site with a relatively simple setup. Although it is not the most accurate method compared to the available methods, it has the advantages of a larger measurement range and anti-inference characteristics. The angular amplifier is made up of two face-to-face plane mirrors with one being fixed and the other being able to rotate. When rotated at an angle of γ by displacement after the light has been reflected N times, its direction will 2886

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deviate from the Nγ angle of the original direction. This is the rotation angle that is amplified N times. After being reflected from the SPR sensor, the phase change of the amplified deviation angle is also amplified N times and greatly increases measurement precision. 2. Principles A. SPR Sensor Phase Measurement Method

Figure 1 shows the experimental structure of the SPR sensor phase measurement method. The heterodyne light source consists of an He–Ne laser, two acoustooptic modulators, two polarization beam-splitters, and two mirrors. The light source is an He–Ne laser with a wavelength of 632.8 nm. By passing through two acousto-optic modulators (AOM1 and AOM2) whose modulation frequencies are 80.0 MHz and 80.01 MHz, respectively, the selected outgoing lights are both the first-order diffraction lights. Adjusting mirrors M1 and M2 to make them coincide and using two polarization beam splitters (PBS1 and PBS2) to split and combine two orthogonal polarized lights achieves a beat frequency of 10 kHz. This is part of the heterodyne light source. The iris shelters the zero order and the other order of lights to prevent their going through the optical system. A beam splitter (BS) divides the heterodyne light source into transmitted light and reflected light. After passing through an analyzer, AN r , with the transmission axis at 45° to the x-axis and then interfering, the photodetector Dr receives the interference signal and converts into an electronic signal [8]. That is the reference signal, I r . It is then input into a lockin amplifier (Stanford Research Systems, model: SR830, phase resolution: 0.01°). The other BS transmission light will pass through the SPR sensor and the interference signal will be received by photodetector Dt after passing through analyzer AN t with the transmission axis at 10° to the x-axis for the purpose of getting larger visibility. The light signal is then converted into another electronic signal and input into the lock-in amplifier. This is the test signal I t . The lock-in amplifier reads the phase difference between the reference signal I r and the test signal I t . The experimental result in Fig. 2 (dotted) shows

Fig. 1. Experimental structure chart of the SPR sensor phase measurement method.

where t is the interval between mirror A and mirror B, and D is the width of mirror A and mirror B. C. Relationship between Displacement and Angle Deflection

Fig. 2. Experimental data (*) and theoretical value (solid) graphs for the SPR sensor’s phase difference and the angle of incidence (exterior angle).

Assuming four reflections between two mirrors (that is an amplification factor of four as shown in Fig. 4), one side of mirror A shall be placed as the axle center, and the other side shall use a movable platform to make small displacement Δz and cause small angle Δγ. The outgoing light will then be 4Δγ from the original outgoing light. In Fig. 4 D is the rotational radius, Δz is the amount of movement, and Δγ is the angle rotation. Their relationship can be described as
⇒ Δγ  tan−1

the relationship between the SPR phase difference and the angle of incidence recorded by rotating the rotation stage. The rotation stage is controlled by the controller (Newport: ESP300). This experimental data (as the symbol *) closely matches the simulation result (solid line) whose gold film thickness is 63.55 nm. The SPR sensor’s feature of being sensitive to angle sensing is used as the basis for measuring angle displacement in this research. B.

Angular Amplifier Principle

As shown in Fig. 3, when mirror A and mirror B face opposite directions while being placed parallel, according to reflection law, when the incidence light is incident to mirror A with α angle, said light will exit with the same angle. When the direction of incidence does not change and the rotation mirror has a γ angle, its reflective angle is α
γ. After being reflected N times, the outgoing light’s angle is α
Nγ [18], which is Nγ deviated to the original outgoing light. This angle deflection is N times to the deflection of the mirror deflecting, so the angle is amplified N times. The relationship between angle of incidence α and the number of reflections N can be written as  
D D −1 < α < tan ; Nt N − 2t

 Δz : D

(2)

This equation shows that angle variation Δγ is in direct proportional to the amount of movement Δz. Its slope Δγ∕Δz  0.00057 deg∕μm when D  10.1 cm, so the amount and direction of displacement can be judged by the positive or negative sign of Δγ. D.

Experimental Structure

Figure 5 demonstrates the method used in this experiment. This structure is divided into three main parts: heterodyne light, angular amplifier and sensing, and phase capturing. Numbers 1–8 are

Fig. 4. Sketch map of the small angle derived by the angular amplifier.


tan−1

Fig. 3. Sketch map of angular magnification.

(1)

Fig. 5. Schematic drawing of the experimental system. 1, He–Ne laser, λ  632.8 nm; 2, 3, polarization beam splitter; 4, 5, 10, 11, mirror; 6, 7, acousto-optic modulator; 8, iris; 9, beam splitter; 12, electric mobile platform; 13, 15, analyzer; 14, 16, photodetector; 17, SPR sensor; 18, rotation stage controller (Newport: ESP300); 19, lock-in amplifier; 20, rotation stage. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS

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considered the heterodyne light part where the frequency difference is 10 kHz. Number 1 is the He–Ne laser with λ  632.8 nm, 2 and 3 are polarization beam splitters, 4 and 5 are mirrors, 6 and 7 are acousto-optic modulators, and 8 is the iris. This method is the same as that shown in Fig. 1. The angular amplifier and sensing part is made up of numbers 10, 11, 12, 17, 18, and 20. Numbers 10 and 11 are angular amplifiers, 12 is the small displacement driving stage, 17 the SPR angle sensor, 20 the rotation stage holding the SPR sensor, 18 is the drive of the rotation stage that can adjust the SPR sensor’s angle of incidence. The phase capturing part is made up of 9, 13, 14, 15, 16 and 19. Number 9 is the beam splitter that divides the light into two light beams, 13 and 15 are analyzers, 14 and 16 are photodetectors, and 19 is the lock-in amplifier. Numbers 13 and 14 produce the reference signal of heterodyne interferometry, and 15 and 16 produce the test signal adjusting the azimuth angles of the transmission axes of analyzers (13 and 15). The best contrast ratio can be found for the two interference signals. The number 19 lock-in amplifier is used for analyzing the phase difference between the two signals. According to the above-mentioned combination and arrangement, the angle of the incidence mirror (11) is selected and the angle of incidence of the SPR sensor (17) is made equal to the resonance angle. The number of reflections, i.e., angle amplification factor N, then needs to be determined for the two mirrored surfaces. Every phase change produced by displacement at one side of the mobile platform loaded mirror (11) of the fixed displacement is recorded. 3. Experimental Results A.

Measurement Results of 0.5 μm Per Step

First, the multiplying power of the angular amplifier was adjusted to seven times and then the angle of incidence of the SPR sensor was also adjusted at resonant angle for measurement. Data was recorded with every 0.5 μm that the platform moved. There are a total of 50 records as shown in Fig. 6(a). The curve shows that this phase is far beyond the SPR sensor’s phase range so the extra phase must have been caused by a mirrored surface. We first assume that the angular amplifier causes the phase change because the angular amplifier is combined with two plane mirrors (10 and 11), which have been made by metallization. The complex refractive index of the metal film will induce the phase shift [9] in the reflection light. To verify that this assumption can be supported, the SPR sensor is first removed, and only the angular amplifier experienced phase change is measured. The result is shown in Fig. 6(b), which proves that our assumption is correct. Then we take the phase value in Fig. 6(a) and deduct the phase value of the angular amplifier in Fig. 6(b) to obtain the curve shown in Fig. 6(c). This phase range is very close to the SPR sensor’s phase range. The angular 2888

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Fig. 6. (a) Every 0.5 μm including SPR’s and angular amplifier’s phase values. (b) Every 0.5 μm including only angular amplifier’s phase value. (c) Only SPR’s phase value (a) with the phase value in (b) deducted.

amplifier’s phase difference is larger than the SPR’s phase difference, which means that the angular amplifier virtually increases measurement sensitivity. B. Standard Deviation

To find the minimum displacement of this driving, the mobile platform (12) continuously measures 100 steps of data both at every 0.1 μm [as shown in Fig. 7(a)] and at every 0.08 μm [as shown in Fig. 7(b)], respectively.

Fig. 8. Comparison of go and back.

C. Multiple Measurement Results with only Angular Amplifier

Fig. 7. (a) Phase value of 0.1 μm of displacement at every step with a total of 100 steps. (b) Phase value of 0.08 μm of displacement at every step with a total of 100 steps.

According to the aforementioned results, the curves in Figs. 7(a) and 7(b) are relatively linear, but the curve in Fig. 7(b) has jumps, and the slope of this line is smaller than that of the line in Fig. 7(a). This finding is due to the mobile platform, which has to overcome the maximum static friction force caused by the weight of the mirror and the mirror base when driving, consequently causing the inconformity of the line’s jumps and slope. Therefore, we only consider the data of 0.1 μm movement at every step and use the following standard deviation to calculate its error and minimum displacement:

Δzmin 

Δϕmin : S

This section deals with only measuring the phase value of the angular amplifier without the SPR sensor, with the multiplying power adjusted to 12 times. With each step of 0.2 μm, a total of 46 steps of measurement data are collected. After a total of 20 repeat times with the same steps, the average data is illustrated in Fig. 8 where ⋄ is the mean value of go after 20 repeat times and * is the mean value of back after 20 repeat times. The principle of magnetic hysteresis involves knowing that there is no full overlap on the path of go and back. The reason for the phenomenon similar to the magnetic hysteresis in this study may

Table 1. Parallel Table of Multiplying Powers with Maximum and Minimum Displacement

N

Δzmax (μm)

Δzmin (μm)

6 8 10 12

1000 200 140 100

1.41 0.92 0.75 0.13

(3)

S is sensitivity, Δϕ is phase value, Δz is amount of movement, Δϕmin is the minimum phase value, and Δzmin is the minimum amount of movement. Among them, the standard deviation is the minimum phase value and S is the slope of the line. From experimental data, Fig. 7(a), the standard deviation is calculated to be 0.58° and slope (S) is −7.71 deg∕μm. Equation (3) can be substituted to get the available minimum displacement of 0.08 μm.

Fig. 9. Multiplying powers corresponding to the maximum movement. 1 April 2015 / Vol. 54, No. 10 / APPLIED OPTICS

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is less sensitive to phase change. Switching to a thinner gold film, such as one of 44 nm, should increase the resolution. This study was supported in part by the National Science Council of Taiwan with contract number NSC 102-2221-E-150-068. References

Fig. 10. Multiplying powers corresponding to the minimum movement.

be the moving of the platform caused by the load effect problem. By calculating the standard deviation and the minimum movement Δzmin with the data in Fig. 8, the standard deviation is determined to be 0.34°, the slope is −2.67 deg∕μm, and the minimum movement is 0.13 μm for the go direction. For the back direction the standard deviation is 0.39°, the slope is 3.03 deg∕μm, and the minimum movement is 0.13 μm. The following maximum and minimum displacements are received by the angular amplifier with different multiplying powers. They are separately compared with 6 times, 8 times, 10 times, and 12 times, as shown in Table 1, and Figs. 9 and 10. All these data are estimated according to the experimental results decided by the critical point of phase jump and the slope of the phase. 4. Conclusions

This study combines an angular amplifier with CPHI and SPR to perform displacement measurements. CPHI has the advantage of being less vulnerable to environmental disturbances, temperature, and vibration. The addition of SPR increases sensitivity; therefore, when the angular amplifier deviates, the phase changes considerably. This experiment proposes using infinitesimal displacements to cause tiny angle changes and then, after enlargement, sensors can receive large amounts of phase shift. Furthermore, this study hypothesizes that due to its easier assembled structure, the mirror phase value can be directly used for tiny angle measurements as well as displacement measurements. Without the SPR sensor the minimum displacement can reach 0.13 μm. After adding the SPR sensor, the minimum displacement can reach 0.08 μm. The maximum measuring range can reach 1000 μm. Since gold is a slightly thick material (∼64 nm), the device

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