Theoretical analysis of sensitivity-tunable total-internal-reflection heterodyne interferometer

Theory and analysis of phase sensitivity-tunable optical sensor based on total internal reflection

The studies conducted on light emitting diode plant factories have mostly adopted hydroponics for convenient nutrient management and pest and disease prevention. In particular, in nutrient management, liquid electrolytes can be measured to determine the aqueous nutrient concentrations and absorption rates as well as electrical conductivity (EC) and pH variations. Precisely controlling the aqueous nutrient contents is crucial to large-scale healthy plant production. However, in most of the current conductivity measurements, electrodes are adopted for determining the nutrient additive concentrations. This approach can be problematic in some cases, such as low electrode sensitivity, which results in nutrient overdose, specifically in nonconductive additives, and hinders plant growth. Therefore, this paper proposes an optical method for measuring the aqueous nutrient contents. In this method, the high sensitivity of common-path heterodyne interferometry is incorporated into aqueous measurements to prevent errors caused by interfering impurities on the electrodes and improve measurement and analytical accuracy. The sensitivity of the sensor used in EC measurements can reach 2300°/mS $\cdot $ cm $^{-1}$ . The method has some merits, e.g., a simple optical setup, high stability etc., high measurement accuracy, high resolution, rapid measurement, and easy operation. In addition, its feasibility is demonstrated.

Application of Total Internal Reflection and Heterodyne Interferometry in Electrical Conductivity Measurements

This paper presents a study of the lateral and axial resolutions of a transmission laser-scanning angle-deviation microscope (TADM) with different numerical aperture (NA) values. The TADM is based on geometric optics and surface plasmon resonance principles. The surface height is proportional to the phase difference between two marginal rays of the test beam, which is passed through the test medium. We used common-path heterodyne interferometry to measure the phase difference in real time, and used a personal computer to calculate and plot the surface profile. The experimental results showed that the best lateral and axial resolutions for NA = 0.41 were 0.5 μm and 3 nm, respectively, and the lateral resolution breaks through the diffraction limits.

Lateral and axial resolutions of an angle-deviation microscope for different numerical apertures: experimental results

This study examines the use of reflectivity-height transformation in full-field angle-deviation microscopes (ADM). In such microscopes, two light intensity distribution images of a prism’s total internal reflection and critical angle are obtained separately with two charge-coupled devices (CCDs), and are converted into a reflectivity profile point-to-point and then into angle of deviation matrix after the beam is reflected by the test sample; finally, the surface height of the sample is found through the triangular geometrical relationship. This method obtains the image through the effective imaging area of CCD. Once the two-dimensional (2D) image is obtained, the third dimension, height, is added to create a full-field 3D surface profile. Its conversion process is nonlinear; therefore, compensation must be made to reduce measurement errors. The optical magnification of high vertical resolution full-field 3D reflection-type ADM could reach >250 times, thus providing submicron measurements with nanometer vertical resolution and allowing for the simultaneous measurement of 2D and 3D images. Small defects on both transparent and nontransparent surfaces can be rapidly detected.

High Vertical Resolution Full-Field Reflection-Type Three-Dimensional Angle-Deviation Microscope with Nonlinear Error Compensation.

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 (approximately 32 nm), nondestructive and noncontact measurement, and larger measurement ranges (+/- 80 microm) for a numerical aperture of 0.21 in a transparent measurement medium. The technique can be used without conductivity and pretreatment.

Transmission-type angle deviation microscopy

A phase geographical map for determining a right-angle prism is presented. The proposed method is based on total-internal-reflection effects and chromatic dispersion. Under the total-internal-reflection condition, the phase difference between the S and P polarizations, as a function of the wavelength and refractive index, can be extracted and measured using heterodyne interferometry. Various wavelengths correspond to various refractive index values. The proposed map is convenient in ensuring the prism material using a specific V number. The method has the following merits: high stability, ease of operation, and rapid measurement.

https://ir.nctu.edu.tw:443/bitstream/11536/11781/1/000240355100019.pdf

Chih-Wen Lai

Papers

Transmission-type angle deviation microscopy

Phase geographical map for determining the material type of a right-angle prism