Abstract:
A new method for measuring refractive index, small angle, pressure or temperature is disclosed. The method of the present invention utilizes a heterodyne interferometry technique to measure the phase difference between s-(vertical) and p-(horizontal) polarizations, and then substitutes the difference into Fresnel&#39;s equations so as to obtain the physical values of the medium to be tested, such as refractive index, small angle, pressure or temperature.

Description:
FIELD OF THE INVENTION 
     The invention relates to an common path heterodyne interferometry, and more particularly, to a total internal reflection heterodyne interferometry (TIRHI) combining total internal reflection characteristics for measuring physical values of a medium to be tested, wherein the two important physical parameters (refractive index and incident angle) can be viewed as physical variations. The method of the present invention is mainly used to measure the physical values such as refractive index, small angle, pressure and temperature of an optic-electro material. 
     BACKGROUND OF THE INVENTION 
     There are a plurality of interferometries and interferometers which are used to make optical and non-contact measurements, but most of the interferometries and interferometers are not in common path structure. Therefore, there are following problems: 
     (1) In a non-common path structure, the optical path difference between the mutually interfered reference beam and test beam should be within the coherent length. Besides, the contrast of the interference signal will decrease when the optical path difference is increased. 
     (2) In a non-common path structure, the environment of the two light beams should be strictly controlled. For example, the air disturbance and the outer vibration should be avoided. Besides, the pressure, temperature and humidity of the control room are also necessary to be controlled stably and effectively. 
     (3) The analysis of the interference fringes is more complex, troublesome and less precise. 
     The heterodyne interferometry carries the physical values to be tested in the phase of the interference signal rather than the amplitude of the interference signal. Therefore, the change of the light intensity during the interfered process will not effect the measurement result. The physical value to be tested can be retrieved from the phase of the interference signal in real time, and this is the unique characteristic of heterodyne interferometry. However, if the heterodyne interferometry is not used in a common path structure, it still has disadvantages such as the above-mentioned (1) and (2) and the measurement precision will be decreased. 
     Refractive index is a very important characteristic parameter of optical materials. There are a plurality of measuring methods proposed such as critical angle method, prism couple method, Brewster angle method and total reflection method. All of these methods utilize the change of the light intensity of the reflection beam or transmission beam to derive the refractive index. However, such methods for measuring the refractive index of the materials to be tested by the light intensity have two main disadvantages: 
     (1) The measurement precision is easily decreased by outer light source or scattering light source when the refractive index is measured by light intensity, thus it is better to measure the medium to be tested in a darkroom so as to isolate the unnecessary light sources. Therefore, it is inconvenient to operate the interferometer in a bright room. Besides, the light source should have a very stable single wavelength. 
     (2) The measurement of the unnecessary reflection light and scattering light among the boundary will be varied by the different incident angles, thus the error compensation of the light intensity will be more troublesome. The measurement precision will be decreased by the light source stability, medium absorption, scattering light and the reflection light from other boundary to be tested. Besides, the refractive index measurement should firstly obtain the thickness of the medium to be tested, and the interference signal is easily effected by the environment disturbance. 
     In the angle measurement, it is conventionally to measure the rotation angle of a medium by mechanic scaling. However, an optical measurement, such as interferometer or autocollimator, is applied when some precision and non-contact requirements are necessary. Though the method has advantage such as high resolution, such a method requires a large space. It is hard to apply such a measurement system in a limit space. 
     SUMMARY OF THE INVENTION 
     In view of the drawbacks of the prior art, it is an object of present invention to provide a measuring method for measuring physical values which are reacted to the refractive index or angle. The relationship between the variation of refractive index or angle and the variation of the phase difference after the total internal reflection is firstly obtained so as to derive the physical value to be tested. Therefore, it is necessary to firstly obtain the relationship between the variation of refractive index or angle and the variation of the phase difference after the total internal reflection. The present invention measures the phase difference which is independent to the light intensity variation and increase the measurement precision. 
     The present invention mainly utilizes a light source with a frequency difference between the s-polarization (vertical) and p-polarization (horizontal) which is incident on the boundary of a prism (the refractive index is known) and the medium to be tested. In this boundary, a phase difference between the s-polarization and p-polarization is generated due to the total internal reflection. Such a phase difference is associated with the refractive index to be tested and the incident angle. The reflection beam after total internal reflecting passes through an analyzer with respect to the transmission axis at 45°, the vectors at 45° of the s-polarization and p-polarization are interfered mutually and are detected by photodetectors. The interference signal is a sinusoidal signal with a frequency difference between two polarizations, e.g. the beat frequency in the interferometry. Such a signal and the reference signal is compared by a phase meter and the phase difference due to the total internal reflection is obtained. The obtained phase difference is finally calculated via Fresnel&#39;s equation operation by a personal computer or an electronic hardware. The refractive index of the medium to be tested is thus obtained in real time. If the refractive index of the medium to be tested is varied, the variation of the refractive index can be derived from the variation of the phase difference. Besides, if the two refractive indexes on the total internal reflection boundary are known, the variation of angle can also be derived from the variation of the phase difference. 
     It is another object of the present invention to provide a method for measuring other physical values such as pressure, temperature and concentrations of liquid and gas. As long as the physical values to be tested will cause the variations of refractive index or angle, the present invention can be applied. 
     It is still further an object of the present invention to overcome the disadvantages of the interferometry or interferometer with non-common path structure and to provide an easy analysis, easy operation, low cost and stable measuring method so as to solve the high precision measurement problems. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings which illustrate one or more embodiments of the present invention. 
     FIG. 1 illustrates a schematic diagram for measuring refractive index or incident angle of the medium to be tested by TIRHI of the present invention; and 
     FIG. 2 illustrates the light path of the total internal reflection at the boundary. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to FIG. 1, the main structure of the present invention are constituted by a light source 11 (heterodyne light source) with a frequency difference between the s-polarization and p-polarization, beam splitter 12, isosceles prism 13, rotary stage 14, two analyzers 16 and 17 with transmission axes at 45°, two photodetectors 18 and 19, phase meter 110, personal computer or automatic operation processing hardware 111 and display 112. The medium to be tested 15 is tightly positioned at the bottom side of the isosceles prism 13. The incident beam is divided into reflection beam and transmission beam. The reflection beam passes through the analyzer 16 and is detected by the photodetector 18 so as to obtain the following mathematical type signal: ##EQU1## wherein is the initial phase difference between the s-polarization and p-polarization, f is the frequency difference between the s-polarization and p-polarization and I r  is the reference signal. On the other hand, the transmission beam passes through prism 13 and is totally internally reflected at the boundary of the medium to be tested 15. The totally internally reflected signal passes through the analyzer 17 and is detected by the photodetector 19 so as to obtain the following mathematical type signal: ##EQU2## wherein I t  is the signal to be tested in the total internal reflection heterodyne interferometry, φ is the phase difference between the s-polarization and p-polarization after the total internal reflection. The signals I r  and I t  are transmitted into the phase meter 110 and are compared so as to obtain the φ. The relation between φ and the refractive index of the medium to be tested can be described as following: 
     Referring to FIG. 2, according to Snell&#39;s law and the light ray refracted into the prism and propagated toward the base surface of the prism; an isosceles prism 21 with known refractive index n 1  and base angle θ p  ; the medium to be tested 22 with refractive index n 2  is tightly positioned on the bottom side of the isosceles prism 21; the s- and p-polarization are incident on one side of the isosceles prism at θ i  ; the incident angle on the boundary is θ 1  ; thus we have ##EQU3## 
     Because the method of the present invention is operated under the total internal reflection condition, the refractive index n 1  should be greater than the refractive index n 2 . According to Fresnel&#39;s equation, the coefficients of reflection of the s-polarization and p-polarization can be respectively expressed as ##EQU4## wherein n=n 2  /n 1  (the refractive index ratio), δ s  and δ p  are the phase delay of the s-polarization and p-polarization generated by the total internal reflection. Therefore, the phase difference between the s-polarization and p-polarization is ##EQU5## 
     Substituting Eq. (1) into Eq. (4), we have ##EQU6## which can be rewritten as ##EQU7## 
     Therefore, the refractive index ratio n can be obtained by the personal computer or automatic operation processing hardware 111 with the measurement of φ and incident angle θ i  measured by the phase meter 110. The refractive index n 2  of the medium to be tested can be further derived. Finally, the result is displayed on the display 112. 
     Similarly, the present invention can be applied to the angle measurement, if the refractive index ratio n is known, we rewritten the Eq. (7) as ##EQU8## 
     Therefore, the angle θ i  can be obtained via substituting the measured by the phase meter 110 into Eq. (9) and (10) and calculating by the personal computer or the automatic operation processing hardware. 
     As to the measurements of other physical values such as pressure and temperature, as long as the physical values will cause the change of the refractive index and incident angle, the present invention can be applied. When the medium to be tested is effected by some physical values and then the refractive index or the incident angle is changed, the physical value of the medium to be tested can be obtained by finding out the relation between the physical variation and the refractive index/incident angle and calculating it via the above-mentioned equations. 
     The present invention firstly discloses a new measuring method which can apply to a plurality of fields. Besides, the present invention is a common path structure. The present invention not only has the advantage of heterodyne interferometry but also overcomes the disadvantages of non-common path structure. Therefore, the obtained result is precise and reliable. Besides, the present invention has high stability against light intensity variation and other scattering light source. Furthermore, the method has several merits such as simple optical setup, easy operation, high measurement accuracy and rapid measurement. 
     Although the present invention and its advantage have been described in detail, it should be understood that various changes, substitutions and alternations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.