1. Millimeter Wave Sensor: An Overview
SURYA K PATHAK
INSTITUTE FOR PLASMA RESEARCH
BHAT, Gandhinagar – , GUJARAT, INDIA

2. Interaction of Electromagnetic Waves with Material Medium
Interaction produces following Physical Phenomenon which are basis of Material characterization
Reflection
Refraction
Attenuation
Scattering
Diffraction
Techniques for Material measurements
Time delay measurements
Phase measurements
Inverse Scattering methods

3. Interferometry and Reflectometry systems
Measurement Mirror
Displacement
Light Source
Beam Splitter
Reference Mirror
Screen/ Detector
Interferometry and Reflectometry is a scientific technique, to interfere or correlate two, or more than two, signals to from a physically observable measure, from which any useful information can be inferred.
Fringe pattern in optical Interferometry
Electrical signals of power/ voltage in
Radio measurement
Michelson Interferometer
Plasma or Dielectric
Quadrature Mixer
Frequency Source
Power Divider
Measurement Path
Antenna
Reference Path I Q
Quadrature Mixer
Frequency Source
Power Divider
Measurement Path
Reference Path I Q
Circulator
Antenna
Plasma or
Dielectric
Interferometer system
Reflectometer system

4. Interaction of Electromagnetic wave dielectrics (1)
The electromagnetic wave incident normally on the dielectric and traveling in z-direction is given by:
(1)
Where  is the propagation constant. On applying boundary conditions across the individual boundaries. Following expressions are obtained in terms of reflected Ei and transmitted Er wave:
(2)
Where 0, and T0 are reflection and transmission coefficient.
Z is the impedance of the medium
Subscript corresponds to respective medium
Dielectric d 2 2 1 1 0 0 Ei Er Et z y

5. Interaction of Electromagnetic wave dielectrics (2)
Solving above equations we can calculate the components of reflected and transmitted wave:
The reflected wave is obtained by
(3)
where,
And the transmitted wave is expressed by
(4)
Wave equations (3) and (4) constructs the measurement path wave in an interferometry

6. Determination of Relative Dielectric constant and Thickness (1)
Complex Permittivity or Dielectric Constant
The relative permittivity or dielectric constant (r) as well as relative permeability (r) characterize the relationship between electromagnetic waves and material properties. For a lossy material, the relative dielectric constant can be expressed as:
(5)
where r is the relative dielectric constant, 0 is the dielectric constant of free space,  is the conductivity of the material, and  is angular frequency of EM waves. Above equation can be represented in terms of loss tangent (which is ratio of imaginary to real component of the complex dielectric constant) :
(6)
Reflection Measurement
In reflection measurement method, the dielectric is typically conductor-backed to increase the reflected power. In this case, Z2 is equal to zero and reflection coefficient in equation (3) is:
(7)

7. Determination of Relative Dielectric constant and Thickness (2)
Impedance Z1 in terms of free space impedance is given by:
(8)
Transmission Measurement
In this method, the dielectric is located in free space between two antennas. Therefore, Z2 = Z0 and 2 = 0 are satisfied, and transmission coefficient is given as:
(9)

8. Determination of Relative Dielectric constant and Thickness (3)
Fig: Phase of reflection coefficient depending on (a) relative dielectric constant
(b) dielectric thickness

9. Determination of Relative Dielectric constant and Thickness (4)
Fig: Phase of transmission coefficient depending on (a) relative dielectric
constant (b) dielectric thickness.

10. Displacement Measurement
The phase difference between the reference and measured paths, produced by displacement of the target location, is determined from in-phase (I) and quadrature (Q):
Where, (t) represents phase difference and can be determined by for an ideal quadrature mixer:
Practically, quadrature mixers, however, have a nonlinear phase response due to their phase and amplitude imbalances as well as DC offset. A more realistic from of the phase including the nonlinearity effect can be expressed as:

11. Displacement Measurement
The detected phase is generated by the time delay, , due to round trip-trip traveling of electromagnetic wave for the distance between antenna aperture and target. Therefore, it has relationship with range, r as:
where, f0 and c are operating frequency and speed in free space of electromagnetic waves. The range as a function of time variable can be defined as :
Range variation is produced by changes in target location and can be expressed in the time domain as:
where, T is the sampling interval. The displacement for the entire target measurement sequence can be described as a summation of consecutive range variations:

12. An Interferometric Sensor*
Fig: Measurement set-up for water level gauging
Heterodyne Interferometric sensor. The target sits either on the XYZ axis (for displacement sensing) or on the conveyor (for velocity measurement). The Reference channel is not needed for velocity measurement.
* Courtesy: Kim and Nguyen, IEEE Trans on Microwave Theory and Techniques, vol.52, p2503, Nov 2004

13. The block diagram of a Ka-band heterodyne measuring setup for lossy dielectric materials.

14. Conclusions Reflectometry is a non destructive sensors
With little modifications it is used in different applications