216
A. Ikehata
d cos δ(sin β + sin α) = mλ
(9.1)
Here, m, is called the order number and represents the integer 0, 1, 2, …. δ is the
angle that the incident or reflected beam makes with the plane perpendicular to the
grooves, and these angles are matched with one another for blaze-type gratings.
δ 1 = δ 2 = δ
(9.2)
The enhanced diffracted light repeatedly appears in the angular direction
depending on the order number. The number of grooves per mm, N, is the most important parameter determining the performance of the grating. Commercially available
blaze gratings often have N = 600 or 1200 grooves/mm. Increasing the number of
grooves reduces the groove spacing and increases the resolution of different wavelengths. Furthermore, the edge angle (blaze angle, θ ) of the groove is an important value in the design of spectrometers. This is defined as the angle at which
the m-th order diffracted light can be obtained with high reflection efficiency. The
wavelength of the light at this angle is called the blaze wavelength. The blaze wavelength and blaze angle define the basic performance of diffraction gratings. When
performing NIR spectroscopy, the blaze wavelength should be in the NIR region. The
reflection efficiency rapidly decreases at wavelengths shorter than the blaze wavelength, but gradually decreases at longer wavelengths. The wavelength range of the
diffraction grating is designed to be one to twice the blaze wavelength. The configuration of the spectrometer using a diffraction grating will be explained in detail in
the next section.
9.1.3.3 Fourier Transform
Fourier transform (FT) spectroscopy is the mainstream technique in the midinfrared region as FT-IR. An FT spectrometer specialized for the NIR region is
also commercially available, called an FT-NIR.
The FT spectrometer measures the interference of light beams divided in two by
use of a double-beam interferometer. Here, we will explain the principle of a doublebeam interferometer using the Michelson interferometer (Fig. 9.5) as an example.
The interferometer consists of a half mirror and two plane mirrors. One of the plane
mirrors can move along the optical axis. Light emitted from the light source is
collimated by the collimator, the beam reflected by the half mirror (HM) goes to
the fixed mirror (M1), and the transmitted beam goes to the movable mirror (M2).
The beams reflected by M1 and M2 are transmitted through, and reflected from,
the opposite surface of the half mirror and combined again. The FT spectrometer
detects the intensity of the combined wave with the detector (D) while changing the
position of M2. The measured intensity increases or decreases with respect to the
position x of the movable mirror, that is, produces an interference waveform, F (x),
called an interferogram. When the light source emits white light, the interferogram
is multiplied by the wavenumber distribution, B (k). In the FT spectrometer, the
A. Ikehata
d cos δ(sin β + sin α) = mλ
(9.1)
Here, m, is called the order number and represents the integer 0, 1, 2, …. δ is the
angle that the incident or reflected beam makes with the plane perpendicular to the
grooves, and these angles are matched with one another for blaze-type gratings.
δ 1 = δ 2 = δ
(9.2)
The enhanced diffracted light repeatedly appears in the angular direction
depending on the order number. The number of grooves per mm, N, is the most important parameter determining the performance of the grating. Commercially available
blaze gratings often have N = 600 or 1200 grooves/mm. Increasing the number of
grooves reduces the groove spacing and increases the resolution of different wavelengths. Furthermore, the edge angle (blaze angle, θ ) of the groove is an important value in the design of spectrometers. This is defined as the angle at which
the m-th order diffracted light can be obtained with high reflection efficiency. The
wavelength of the light at this angle is called the blaze wavelength. The blaze wavelength and blaze angle define the basic performance of diffraction gratings. When
performing NIR spectroscopy, the blaze wavelength should be in the NIR region. The
reflection efficiency rapidly decreases at wavelengths shorter than the blaze wavelength, but gradually decreases at longer wavelengths. The wavelength range of the
diffraction grating is designed to be one to twice the blaze wavelength. The configuration of the spectrometer using a diffraction grating will be explained in detail in
the next section.
9.1.3.3 Fourier Transform
Fourier transform (FT) spectroscopy is the mainstream technique in the midinfrared region as FT-IR. An FT spectrometer specialized for the NIR region is
also commercially available, called an FT-NIR.
The FT spectrometer measures the interference of light beams divided in two by
use of a double-beam interferometer. Here, we will explain the principle of a doublebeam interferometer using the Michelson interferometer (Fig. 9.5) as an example.
The interferometer consists of a half mirror and two plane mirrors. One of the plane
mirrors can move along the optical axis. Light emitted from the light source is
collimated by the collimator, the beam reflected by the half mirror (HM) goes to
the fixed mirror (M1), and the transmitted beam goes to the movable mirror (M2).
The beams reflected by M1 and M2 are transmitted through, and reflected from,
the opposite surface of the half mirror and combined again. The FT spectrometer
detects the intensity of the combined wave with the detector (D) while changing the
position of M2. The measured intensity increases or decreases with respect to the
position x of the movable mirror, that is, produces an interference waveform, F (x),
called an interferogram. When the light source emits white light, the interferogram
is multiplied by the wavenumber distribution, B (k). In the FT spectrometer, the