Temperature modulated refractive index measurement
The present invention is directed to temperature modulated refractive index measurement. In accordance with the invention a method for determination of the complex temperature coefficient of the refractive index of a sample is provided, wherein the determination of the complex temperature coefficient of the refractive index of the sample is based on a refractive index measurement. Furthermore, the refractive index of the sample is measured over a period of time, wherein the temperature of the sample is modulated over said period of time and the complex temperature coefficient of the refractive index is calculated on the basis of the refractive index measurement over the period of time and the temperature modulation over the period of time. Additionally, a measurement system, in particular comprising a temperature control system and a processing system to carry out the above method, is disclosed.
1. A method for determination of a temperature coefficient of a refractive index of a sample, wherein the determination of the temperature coefficient of the refractive index of the sample is based on a refractive index measurement, said method comprising:
measuring a refractive index of the sample over a period of time, wherein a defined temperature of the sample is modulated over the period of time;
measuring the modulation of the temperature over the period of time; and
calculating a temperature coefficient of the refractive index based on the sample's refractive index measurement over the period of time and on the measured temperature modulation over the period of time.
2. The method in accordance with claim 1 , wherein an amplitude of the temperature modulation is small such that a linear response of the refractive index is provided and the temperature coefficient of the refractive index can be described by the equation
Φ
*
(
ω
)
=
ⅆ
n
*
ⅆ
T
(
ω
)
,
wherein n* is the complex refractive index, T is the temperature, and ω denotes the frequency of the temperature modulation.
3. The method in accordance with claim 2 , wherein the calculation of the temperature coefficient of the refractive index comprises using at least a partial Fourier transformation of the refractive index measured over the period of time and of the temperature modulation over the period of time.
4. The method in accordance with claim 3 , further comprising calculating the phase and the amplitude of each frequency component of the Fourier transform.
5. The method in accordance with claim 3 , wherein at least one of:
the amplitude of each frequency component of the refractive index Fourier transform is divided by the amplitude of the respective frequency component of the temperature modulation Fourier transform, and
the phase of each frequency component of the temperature modulation Fourier transform is subtracted from the respective frequency component of the refractive index Fourier transform.
6. The method in accordance with claim 1 , wherein at least one of:
an amplitude of the temperature modulation is smaller than 1 K,
the amplitude of the temperature modulation is within the range of 0.01 K and 0.5K, and
the temperature is modulated with a resolution of at least 0.01 K.
7. The method in accordance with claim 6 wherein the temperature modulation comprises at least one of: a rectangular modulation, a sinusoidal modulation, a saw-tooth modulation, a stochastic modulation, or a multi-frequency modulation.
8. The method in accordance with claim 7 , wherein the temperature is kept essentially, spatially constant over the complete sample.
9. The method in accordance with claim 8 , wherein at least one of:
the modulation frequency of the temperature is in the range of 10 −3 Hz to 10 Hz, and
the modulation frequency of the temperature is between 10 −2 Hz and 1 Hz.
10. The method in accordance with claim 9 , wherein the measuring of the refractive index of the sample over a period of time is carried out for different frequencies of temperature modulation, such that a frequency spectroscopy of the temperature coefficient of the refractive index is obtained.
11. The method in accordance with claim 10 , whereas the sample is subject to at least one of:
a solid-liquid transition phase transition during measurement,
a glass transition during measurement,
an evaporation during measurement, and
a polymerization.
12. The method in accordance with claim 11 , further comprising changing at least one of the temperature and a pressure within the period of time with a frequency being at least one of at least one decade lower than the modulation frequency of the temperature, and at least two decades lower than the modulation frequency of the temperature, such that one of a quasi-isothermal and a quasi-isobaric measurement of the temperature coefficient of the refractive index is obtained.
13. The method in accordance with claim 12 , wherein the method further comprises determining a coefficient of thermal expansion utilizing the equation
α
*
(
ω
)
=
-
6
n
0
(
n
0
2
+
2
)
(
n
0
2
-
1
)
Φ
*
(
ω
)
,
wherein α*(ω) is the complex coefficient of the thermal expansion; n 0 is the equilibrium refractive index; and Φ*(ω) is the complex temperature coefficient of the refractive index; and ω is the modulation frequency of the temperature modulation.
14. The method in accordance with claim 13 , wherein the refractive index of the sample is measured over the period of time utilizing a refractometer system comprising:
a light source,
a prism,
a detector,
a temperature control system, and
a processing system,
wherein the sample is adjoining the prism, and wherein
the light source, the prism, the sample, and the detector are structured and operable to generate a beam of light, with an optical wavelength, passing through the prism to the sample, and to detect at least a part of the beam of light reflected by the sample by the detector, and wherein
the temperature control system is operable to modulate at least the temperature of the sample over the period of time, and
the processing system is operable to measure the refractive index over the period of time and calculate the temperature coefficient of the refractive index on the basis of the refractive index measurement over the period of time and on the basis of the temperature modulation over the period of time.
15. A measurement system for determination of the temperature coefficient of the refractive index of a sample, said system comprising:
a light source, a detector system, and optical elements, wherein the light source, the sample, the optical elements and the detector system are structured and operable to measure the refractive index of the sample;
a temperature control system structured and operable to modulate a defined temperature at least of the sample over the period of time;
a temperature sensor system for measuring the modulation of the temperature; and
a processing system structured and operable to determine the temperature coefficient of the refractive index based on the refractive index measurement over the period of time and on the temperature modulation as measured by the temperature sensor system over the period of time.