Simple refractometry using optical path separation via multiple pinholes
© The Author(s) 2017
Received: 15 November 2016
Accepted: 13 January 2017
Published: 24 January 2017
We herein report on a simple and novel method of refractometry that uses a micro image defocusing technique. This simple method makes use of a three-pinhole aperture attached to a microscopic optical system. In order to develop our proposed method, an analytical formula was derived from the principles of optical modelling, taking into consideration imaging optics, and was verified experimentally. In order to verify and demonstrate the method, the refractive index (RI) of several materials with known and certified RIs were measured. The results demonstrate a good level of accuracy, with a difference between the certification and the measurements of the order of 10−4 RIU (refractive index unit).
KeywordsRefractometry Refractive index Multiple pinholes
Refractive index (RI) of the fluid is one of the optical properties that can be used to infer various biological and chemical properties of a material, and that refractometry therefore has great potential for use in biological and chemical applications as a highly sensitive, label-free, optical sensor [1–4]. The significant advantages of such an optical sensor have led to the development of various kinds of refractometries in order to meet the requirements of different applications over the last half-century. New concepts of refractometry continue to be proposed widely, as the importance of label-free sensing in bio-chemical, bio-medical, ecological, and food applications increases.
An image defocusing technique has been used in Defocusing Digital Particle Image Velocimetry (DDPIV) for 3D particle tracking and 3D flow measurement [5, 6]. This imaging technique has been extended to microflow applications such as the micro image defocusing technique [220.127.116.11]. Within this field, several authors have described the effects of fluid RI in the image defocusing for the purpose of z-compensation for fluid RIs when using (μ−) DDPIV [6, 9, 10]. It is therefore plausible that the image defocusing technique might be applied to the measurement of RI using a simple optical layout. A micro-refractometer that used micro image defocusing and a microfluidic device was reported previously  but the authors gave no details of its optical configuration; however, they demonstrated the use of the image defocusing technique for RI measurement.
We herein propose a new RI measurement method that utilizes the image defocusing technique in conjunction with a three-pinhole aperture, but in a different way from the aforementioned micro-refractometer . While the previous study used the direct comparison of the image separation, we suggest a method that utilizes the change rate of the image separation. This method might have a wider range of applications due to its insensitivity to uncertainties in the environment, such as the working distance, sample thickness, and substrate material.
Micro image defocusing & working principle for the measurement of RI
The image separation, D, which is defined to be the diameter of the circle circumscribed around the three defocused spot images [7, 10, 11], is mainly determined by the working distance, the thickness of the sample, the pinhole separation, and the RI of the sample. Once all of the parameters, with the exception of the sample RI, have been fixed, the image separation becomes a function of the RI alone. Thus, RI measurement using the image defocusing technique is possible by calibration across different values of RI and D. There are, however, a few practical difficulties associated with maintaining consistency of the working distance and the sample thickness between the calibration procedure and RI measurements. In light of these difficulties, we use the relationship between the RI of the sample and ΔD/Δz. This is possible because ΔD/Δz is almost constant due to the linear nature of the z–D relationship, and is independent of both the working distance and thickness of the sample [7, 9].
The aperture with the three pinholes was fabricated by means of a Si-DRIE (Deep Reactive-Ion Etching) process. The three pinholes each had a diameter of 1.5 mm and were aligned equilaterally. The diameter (d) of the circle circumscribed around the three pinholes was defined to be the pinhole separation, and was limited by the opening diameter of the objective lens. The pinhole separation was 4.0 mm in the present study. The spot-patterned glass plate was prepared by chrome sputtering and wet etching. The transparent spots each had a diameter of 3 μm and were evenly distributed in a pattern with 50 μm lateral and longitudinal spaces on the opaque chrome surface. For accurate analysis, the intensity peaks of the spot images were determined using the Gaussian sub-pixel searching method. Certified liquids (Cargille Labs Inc., USA) with known RIs (n D) of 1.300, 1.400, 1.500, 1.600, and 1.700 at 25 °C were used for calibration; these values had a variation of 0.0002 RIU. Room temperature was controlled at 25 °C.
Result and discussion
Results of RI measurements
Certified RIs (Cargille labs Inc.)
RI liquid 1
RI liquid 2
RI liquid 3
A simple method for refractometry that utilizes an image defocusing technique with a 3-pinhole aperture has herein been proposed. For the proposed method, analytical formulae were derived by considering the imaging optics, and these were verified experimentally. The resultant formula, which can be further used in calibration, is given as \(n = C/(\partial D/\partial z)\) where the constant, C, was determined to be 2.183 RIU (pixel/μm) for the optical layout used in the present study. Using this calibration function, the image defocusing technique was used to measure the RI of a range of materials with certified RI values. The demonstration showed a good accuracy with a difference of the order of about 10−4 RIU between the certified and measured values. The proposed refractometry therefore has the potential to be used as a simple method for the measurement of RI values in both liquid and gel materials. Due to its simple optical layout, the proposed refractometry could be reasonably accessible to most laboratories, and would be a good option for many RI-based sensing applications.
SYY and JCH has fabricated the device, also carried out the experimental study and drafted the manuscript. SY supervised the project and completed the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
This material is based upon work supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2016M3A7B4910556) and the Industrial Technology R&D program of MOTIE/KEIT. [2016 (No.10062533)].
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