Transmission-type angle deviation microscopy Ming-Hung Chiu,1,* Chih-Wen Lai,2 Chen-Tai Tan,2 and Chin-Fa Lai2 1
2
Department of Electro-Optical Engineering, National Formosa University, 64 Wunhua Road, Huwei Yunlin 632, Taiwan
Institute of Electro-Optical and Materials Science, National Formosa University, 64 Wunhua Road, Huwei Yunlin 632, Taiwan *Corresponding author:
[email protected] Received 16 June 2008; revised 4 September 2008; accepted 9 September 2008; posted 11 September 2008 (Doc. ID 93666); published 8 October 2008
We present a new microscopy technique that we call transmission angle deviation microscopy (TADM). It is based on common-path heterodyne interferometry and geometrical optics. An ultrahigh sensitivity surface plasmon resonance (SPR) angular sensor is used to expand dynamic measurement ranges and to improve the axial resolution in three-dimensional optical microscopy. When transmitted light is incident upon a specimen, the beam converges or diverges because of refractive and/or surface height variations. Advantages include high axial resolution (∼32 nm), nondestructive and noncontact measurement, and larger measurement ranges (80 μm) for a numerical aperture of 0.21in a transparent measurement medium. The technique can be used without conductivity and pretreatment. © 2008 Optical Society of America OCIS codes: 120.0120, 040.2840, 050.5080, 180.5810, 120.3180, 240.6680.
1. Introduction
The majority of developments in optical microscopy in recent years were plotted by Garini et al. [1] and divided into two- and three-dimensional measurements. Several techniques, such as near-field scanning optical microscopy (NSOM) [2,3], total internal reflection fluorescence (TIRF) [4], and surface plasmon resonance (SPR) [5] are now used for surface measurements. The measurement range extends from several micrometers to nanometers. Three-dimensional measurements include conventional and confocal microscopies. Most of the digital images measured with a conventional microscope use a charged-coupled device (CCD). The resolution depends on the system multiplication and CCD pixel size. Nonlinear techniques, such as multiphoton [6], e.g., two-photon (2P) and three-photon (3P), second harmonic generation (SHG), along with interference [7] and deconvolution [8] methods, are implemented in conventional microscopy to improve lateral resolu0003-6935/08/295442-04$15.00/0 © 2008 Optical Society of America 5442
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tion. Confocal microscopy [9] is widely used in biology because of its good axial resolution. In 1988, Kohno et al. [10] proposed a practical high precision optical surface sensor (HIPOSS) based on the critical angle method, using the steep reflectivity change characteristics around the critical angle for high precision surface roughness measurements. These experimental results demonstrated that the displacement resolution was better than 1 nm. In 2006, Wang et al. [11] proposed a SPR angular sensor for measurement of small angle displacement in the phase method. Combining the HIPOSS and small angle measurement concepts, in 2007 we proposed a new technique, designated angle deviation microscopy (ADM) [12], for three-dimensional measurement. ADM is a reflection method whose axial resolution is capable of reaching to the nanometer scale. We have continued our research into the ADM and now propose a transmission angle deviation microscopy (TADM) for the measurement of a transparent sample. The method is based on common-path heterodyne interferometry and the use of a SPR sensor. Scanning the specimen will yield the profile of the surface or refractive index.
2. Principles
From Fig. 1, the experimental setup shows that a beam from a heterodyne light source [13] with a wavelength of 632:8 nm, two orthogonal polarizations ( an s and a p), and a beat frequency of 2 kHz was incident upon a beam splitter (BS). The heterodyne light source is composed of a He–Ne laser, an electro-optic (EO) modulator, and a polarizer. The beam from the heterodyne light source was split into two beams: reflection and transmission. The reflection beam went through an analyzer (ANr) and was detected by a detector (Dr). The result is a reference signal that was used to calibrate the initial phase shift of the measurement system. The transmission beam is a test beam, which was extended by a beam expander, entered the first objective lens, and then focused on a specimen. As the beam passed through the specimen that was also on the focal plane of the second objective lens, the beam was a plane wave and incident upon a SPR sensor. Thus there was no angle deviation. If the specimen has a surface height variation, the beam from the second objective lens converges or diverges. The test beam from the output of the SPR sensor also passed through another analyzer (ANt) and was detected by use of a photodetector array (PDt). All the phase differences were measured with a lock-in amplifier. The TADM system utilized the two polarized heterodyne rays of the test beam to measure the phase difference between them and then obtain the surface height. When the surface height of the scanned point varied, the transmitted beam after the second objective lens either converged or diverged, and the deviation angle was sensed by use of a SPR sensor and two
elements (A and B) of a PDt. Similar to the signal process in ADM [12], the phase difference between these two detected signals is measured using a lock-in amplifier and is proportional to the angle deviation that is due to the surface height or refractiveindex variations. In our adopted four-layer SPR sensor [12] (BK7 glass prism–Ti–Au–air) with a Kretschmann configuration, normally, n1 , n2 , n3 , and n4 are used to represent the refractive indices of the prism, Ti, Au, and air, respectively. The purpose of using the Ti film is to increase the adhesive force between the Au film and the prism. Based on the SPR principle, the surface plasmon waves are excited when incident angle α is equal to the resonant angle αsp . The resonant angle αsp is written as αsp ¼
sin−1
1 ε3 ε4 1=2 ; n1 ε3 þ ε4
where ε3 and ε4 are the permittivities of Au and air, respectively. From the Fresnel formulas, the reflection coefficients of p and s polarization can be expressed as rt ¼ jrt j expðiδt Þ;
t ¼ p; s;
ð2Þ
and the phase shift between them is given as ϕ ¼ δp − δs : 3.
ð3Þ
Results and Discussions
In our experiment, the Ti and Au thicknesses of the four-layer SPR sensor are 2.5 and 44:3 nm, respectively. The permittivities of the BK7 glass prism, Ti, Au, and air at wavelength λ ¼ 632:8 nm are ε1 ¼ ð1:51509Þ2 , ε2 ¼ −3:84 þ 12:5i, ε3 ¼ −12 þ 1:26i, and ε4 ¼ ð1:0003Þ2 , respectively. Therefore, the resonant angle αsp is equal to 43:85°. If the incident angle is rotated to α ¼ αsp and the specimen is located at the focal plane, then the two marginal rays (rays A and B in Fig. 1) of the test beam have no angle deviation and possess identical phase shifts (ϕA ¼ ϕB ). Thus Φ ¼ ϕA − ϕB is equal to zero. If the specimen is out of the focal plane, e.g., Δz > 0, as shown in Fig. 2(a), these two marginal rays [where ray A with positive deviation angle (Δθ) and ray B with negative deviation angle (−Δθ)] have the same phase deviation but with opposite sign. From Fig. 2(a), surface height Δz causes ray B from the second objective lens to have a negative angle deviation. For a smaller NA value, the surface height is given by −f 2 2n D n Δz ≅ Δθ ≅ − Δθ; D n−1 2NA2 n − 1
Fig. 1. TADM experimental setup.
ð1Þ
ð4Þ
where Δz is the distance from the specimen to the focal plane, f is the focal length of the objective lens, D is the distance between two rays, Δθ is the deviation angle from the optic axis, and n is the refractive index 10 October 2008 / Vol. 47, No. 29 / APPLIED OPTICS
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Fig. 2. (Color online) (a) Beam divergence that is due to increased surface height (Δz > 0). (b) Beam convergence that is due to decreased surface height (Δz < 0).
of the specimen. From Eq. (4), the relation between Δz and Δθ is almost linear. For the reasons mentioned above, the phase difference (Φ ¼ ϕA − ϕB ) is proportional to the angle deviation (Δθ) and surface height (Δz). The numerical simulation results of Φ versus Δz are shown in Fig. 3. There are several lines in Fig. 3 that represent the estimation of the different NA values. For example, for a NA of 0.25 for the phase
Fig. 3. Simulation results of phase difference Φ versus surface height Δz for different NA values. 5444
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range of 100°, the maximum surface height is in the region of 80 μm. In other words, if Δz < 0, as shown in Fig. 2(b), the value of Φ is negative. For the first experiment with TADM, we used two objective lenses with the same numerical aperture (NA of 0.21) and a test beam size of 7 mm to demonstrate our idea. Based on the principle of the diffraction limit, the spot size at the focal plane was approximately 1:84 μm. For the periodic pattern such as a grating, we could use the spot size to scan the pattern and achieve the initial results. We set the test beam to progress in the z direction and the scan direction lay along the x − y plane. The transparent specimen was placed on a piezoelectric transducer (PZT, Jena Model 70585) and positioned to the right at the focal plane. Each scan step along each axis was 0:1 μm; the scanned area was 5 μm × 5 μm. We used a 600 line=mm optical grating (manufactured by Thorlabs, Newton, New Jersey) for the test. The interval between two grooves is approximately 0:8 μm, so it is impossible to scan a single groove unless the pattern has only one groove or the NA value is high enough (i.e., the spot size is less than the groove width). Three-dimensional experimental results from TADM are shown in Fig. 4, and the two-dimensional results from TADM and atomic force microscope (AFM) are shown in Figs. 5(a) and 5(b), respectively. There are several points in the TADM results with negative surface height values. That is to say that the focal plane is not just at the valley of the groove. Thus, for the ground level, i.e., the focal plane, most points are higher than the ground and the others are lower ; we could fine tune the focal plane to offset the ground. Figure 5 shows a comparison of the results obtained with TADM and the AFM, which shows that the TADM profile closely coincides with that of the AFM. Two measurement results have the same groove interval and depth. The groove depth and interval are approximately 400 nm and 0:8 μm, respectively, which demonstrates the feasibility of the TADM. We were able to distinguish the peak from the valley in each scan line in the TADM results, which yielded a lateral resolution of almost 0:8 μm.
Fig. 4. Three-dimensional measurement results from the TADM with a NA of 0.21 for a 600 line=mm grating.
axial resolution is close to 32 nm and the lateral resolution is near 0:8 μm for a NA of 0.21. It is obvious that the lateral resolution is better than the diffraction limit value of 1:84 μm. Under the same environmental conditions, if the NA value is larger, e.g., 0.85, the axial resolution is estimated to be 2 nm and the lateral resolution is enhanced. This study was supported in part by the National Science Council of Taiwan under contract NSC 95-2221- E-150-076. References
Fig. 5. (Color online) Two-dimensional measurement results from (a) the TADM and (b) the AFM.
4. Conclusion
In our method, the profile is proportional to capturing the phase difference between the two marginal (edge) rays of the test beam. The two edge rays approach each other and the optical paths are almost the same. The advantages of the nearly commonpath optical structure are that it offers higher stability and independence from environmental disturbances, temperature variation, and other problems. In conclusion, for the periodic pattern, the
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