Fast defect measurements based on the critical angle principle and the use of a CCD camera Ming-Hung Chiu*, Zhen-Chin Lin and Teh-Chao Liao Department of Electro-Optical Engineering, National Formosa University No.64 Wunhua Road, Huwei Yunlin 632, Taiwan R.O.C. *Corresponding author: Tel.: +886-5-6315666, Fax: +886-5-6329257 E-mail address:
[email protected]
ABSTRACT A new method for measuring the optical defects rapidly based on the critical angle principle and the use of a CCD camera is presented. A light with the p-polarization was normally incident into a test plate and passing through a parallelogram prism at the critical angle. If the plate has some defects, a light passing through the defect point will deflect a small angle and then the output intensity from the prism is varied suddenly. The variation of intensity is function of the surface height. Using a CCD camera to record the intensity pattern of the test surface is a new idea for measuring the surface profile. INTRODUCTION A low-cost measure with a higher resolution and a real-time measurement is very important for now the precision industries. A non-destructed method like as the optical method is preferred. In 1969, I. J. Hodgkinson [1] proposed a new optical method that he took some pictures for recording the interference patterns in order to analyze the surface profile of the coated optical surface. The roughness resolution is better than λ / 10。In 1972, Robert A. Sprague [2] proposed the concept of space coherence for surface roughness measurement. The visibility of the spot is function of the roughness. In 1998, Zu-Han Gu [3] used the method of angular memory line to detect the surface roughness at some different sight angles by using a CCD camera. In 2000, Luis Miguel Sanchez-Brea et al[4] proposed an intensity technique for detecting the surface defects on the metal lines with the diameter of 50~2000 µm，the intensity of the scattering light is directly decided the situation of the surface defects. PRINCIPLES 1. A beam deflected from a transparent plate that with a small apex angle
As a light is incident into a transparent plate, the plate with a small apex angle is shown in Fig. 1. We denote the small apex angle, the incident angle at the first interface, and the second interface refraction angle as , i1 , and t 2 , respectively. From geometrical optics, the angular deviation is written as (1) i1 t 2 . If the light is normally incident into the first interface, i.e. i1 0 and t 2 sin 1 n sin , where n is the refractive index of the plate and 0 , the angular deviation may be rewritten as (2) (n 1). It is evident that the angle deviation is directly proportional to the apex angle. Therefore, we can obtain the apex angle by measuring the angular deviation when the refractive index n is known. 2. Critical Angle Principles In Figure 1, a laser beam from air( n2 =1.0003) is incident into an right-angle prism with a refractive index of n1 ( n1 1.51509 ). According to t he Snel l ’ s law, the incident angle at the hypotenuse surface is given as n2 sin , (3) 1 45sin 1 n 1 where is the incident angle at the first plane of the prism. As the angle 1 is equal to the critical
n angle c ( c sin 1 2 n 41.317), then is equal 1 to 5.585. From the Fr esnel ’ s equat i ons, t he reflective coefficient of the P-polarized light is give as n cos 1 n1 cos 2 rp 2 , (4) n2 cos n cos 1 1 2 where 2 is the refraction angle. And the reflectivity of the P-polarized light for one reflection is written as 2
R p rp .
(5)
If the prism has two reflections with the same incident
angle, the total reflectivity is written as
R p 2 r 2 p
2
.
(6)
We set that the angle of is at the region of -6°~-5°, the refractive indices n1 =1.51509 and n2 =1.0003. Substituting these values into Equations (3)~(6), the curve of reflectivity of R p 2 is shown in Fig.3. Because the reflectivity is proportional to the angle of and the best sensitivity of intensity measurement is near at the critical angle, we set the point 5.585is to be a reference point for angular measurement. The reflectivity is measured, the angle of is obtained. Because the variation is equal to the deviation angle and from Equations (1) and (2), the angle is proportional to the apex angle . Thus, from the description mentioned above, the apex angle can be calculated and the defect will be detected. 3. Experimental Setup The optical setup is shown in Fig.4. A He-Ne laser beam was expanded by using a beam expander which consisted of two lenses and a pinhole. The expanded beam was passing through a polarizer PL(0°)to obtain the P-polarized light and then the beam was incident into a parallelogram prism near at the critical angle. The output intensity was detected by using a CCD camera. The intensity was adjusted by rotating an analyzer (AN) for avoiding the intensity saturation of CCD. The sample was inserted between the PL and the prism, and the beam was normally incident to the sample. Before inserting the sample, the reflectivity R p 2 was adjusted by rotating a rotation stage for seeking for the critical angle. The initial intensity pattern like as a reference pattern was recorded by using the CCD camera. After the sample inserted, the another intensity pattern like as the test pattern was also recorded. Comparing these two patterns, the intensity difference ratio was obtained and plotted in a personal computer (PC). The defect locations can be pointed out in the diagram. RESULTS AND DISCUSSIONS According the experiment setup in Fig.4, a plate before scraped was in test and the recorded reference pattern was shown in Fig.5. Another intensity pattern from the tested plate after scraped was shown in Fig.6. The intensity difference pattern between two patterns is shown in Fig.7. This is a surface defect pattern. Form the intensity difference pattern, the large intensity difference area can point out immediately. We used an optical microscope to view the plate after scraped. The scraped shape was recorded in Fig 8.
Comparing Figures 7 and 8, the scraped shapes were the same. Thus feasibility of the method for quickly detecting the optical components is demonstrated. CONCLUSIONS We proposed a new optical method for rapidly measuring the surface defects. The method combines the critical angle principle and a CCD camera. From our results, its feasibility is demonstrated. The technique has some merits such as high sensitivity, low cost, easy operation, simple structure and on–line rapid detection. References [ 1]I .J .Hodgki nson,“ A Met hod f orMappi ng and Determining the Surface Defects Function of Pairs Coat ed Opt i calFl at s“ ,Appl. Opt. 8,1373-1378, 1969. [2] Robert A. Spr ague, “ Sur f ace r oughness measur ementusi ng whi t el i ghtspeck l e“ ,Appl. Opt. 11, 2811-2816, 1972. [3] Zu-HanGu,” Det ec t i onofasmal ldef ec tona r oughsur f ace” ,Optics Letters, 23, 494-496, 1998. [4] Luis Miguel Sanchez-Brea, Philip Siegmann, Maria Aurora Rebollo, and Eusebio Bernabeu, “ Opt i cal t echni quef ort heautomatic detection and measurement of surface defects on thin met al l i cwi r es” ,Appl. Opt. 39, 539-545, 2000.
n i 1
t 2
Fig.1: An angular deviation of a beam.
2
n2 1
n1
n2
Fig. 2: A light is incident into a prism.
v.s. Rp2 1.1 1 0.9
Rp2
0.8 0.7 0.6 0.5 0.4 -6
-5.8
-5.6 -5.4 (degree)
-5.2
-5
Fig. 3: The simulation curve of R p 2 versus the incident angle
Lens
Fig. 6: The test pattern recorded from the CCD camera
Rotation stage Parallelogra m PL(0°) Prism AN
He-Ne Laser CCD
Isolator
Sample
Pinhole
PC
Two-axis linear stage
Fig. 7: The defect measurement results from the proposed method
Fig. 4: Experimental setup
\ Fig. 5: The reference pattern recorded from the CCD camera
Fig. 8: The defect measurement results from an optical microscope
