{'fraction_non_alphanumeric': 0.022257782950247308, 'fraction_numerical': 0.012219959266802444, 'mean_word_length': 4.366900858704137, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Study of the Composition and Spectral Characteristics of a HDG-Prism Disperse System (GRISM) by Refractive Index Phase Matching

The composition and characteristics of a GRISM gained by refractive index matching between a refractive index modulation type HDG and a prism is investigated, the HDG being built by processing silver halide emulsion with halide vapor. The GRISM has been stable under external influences like humidity or ultraviolet light exposure. The mercury atomic spectrum obtained by a GRISM based on a HDG with a spatial frequency of 600mm-1 shows yellow dual lines with the wavelength difference of 2.1nm sufficiently separated.


Introduction
We have used a holographically obtained phase transmittance type holographic diffraction grating (HDG) as the main disperse unit and integrated it with a wedge prism, using a phase matching method with the consideration of the refractive index of each element, to compose a transmittance type GRISM. It is a straight-line disperse unit useful in a direct vision spectroscope.
Then we have commenced a research to examine its spectral characteristics.
Usually a disperse unit obtained by the integration of a HDG and a prism is called a GRISM. [1] Since it has a number of advantages, many studies of its development and use have been published. [2,3] In reference [2] we can find the results of a study on a prism type disperse unit which has a grating pattern covering one of its faces, while reference [3] introduces an application method of a GRISM to a telescopic optical system.
The most common processing method in building a HDG with silver halide emulsion is the method using R-10(KBr) bleach agent. [4,5,6] Usually this method results in a surface relief type HDG. [6,7,8] A phase type HDG obtained by such bleaching method is known to be vulnerable to external environments like ultraviolet exposure. [9,10,11] Our first step in making a GRISM was to obtain a phase type HDG using Br 2 halide steam processing method. [12,13] We have used "лои-2" plate, a silver halide emulsion as the base and processed it with "Kodak D-19" to obtain an amplitude grating. Then we have processed it with Br 2 to obtain a refractive-index modulatied phase type HDG. Such a HDG retains micro-scaled relief on its surface which has been existing before the halide steam processing, but it becomes a phase type grating having refractive-index modulation in the emulsion as its main modulation factor. In this case, a phase type HDG with the spatial frequency of 600mm -1 has a maximum diffraction efficiency of 60~75%.
During the design of a GRISM as a straight-line disperse unit, we must rationally select geometrical dimensions like the apical angle of the prism.

Fraunhofer diffraction in a prism-slit disperse system
First, we will discuss the phenomena occuring in an optical system consisting of a slit and a prism, instead of a HDG.
Consider an optical system like figure 1 where a slit of width a 0 is attached to a wedge type rectangular prism and let the incident light be a plane light wave. In this condition the light wave entering this system is bound to undergo a continuous phase-change along the slit face. Let the center of slit be the origin of coordinates and assume that the apical angle δ of the prism is not large. Now, at coordinate y the prism's geometric thickness is y a δ δ + 2 0 and its optical thickness is where n is the refractive index of the prism's material. The according phase change where . The first term of Eqs. 1 is the phase change through the prism and the second term is the phase change caused by the optical path 0 δa .
If we consider the Fraunhofer diffraction pattern gained by the slit alone without a prism, since the wave amplitude of a part of the slit of width dy is 0 0 a dy A , the light's complex amplitude gained by the superposition of these waves can be described as the following.
If a prism is put before the slit, the amplitude of the light wave diffracted by the slit will undergo a phase change as described in Eqs.
and if we put we get the following. we can get from Eqs. 5 the conclusion that the primary maximum of the diffraction pattern would deviate as much as δ ϕ from the principal axis in a prism-slit optical system.

Design and composition of a GRISM by refractive index matching
We can use Eqs. 7 to design and compose an optical system where Bragg's diffraction angle for maximum diffraction efficiency is balanced by a prism. In more detail, we must compose the system so that the deviation angle ϕ is balanced by the diffraction angle 1 ϕ of the HDG which gives the first order diffraction spectrum, namely the condition 1 ϕ ϕ = must be satisfied.
Maximum condition of the diffraction pattern of a refractive index modulation type HDG is satisfied when incident light has Bragg angle as its incident angle.
The Bragg angle can be described as For the given HDG-prism disperse system it follows from Eqs. (7)~(10) that We derive from Eqs. (11) that the spatial period Λ of the HDG and the apical angle δ of the prism should satisfy the following condition.
The relationship between the spatial period of the HDG and the apical angle of the prism is shown in Fig. 3. We can learn from Fig 3. that in case of has been conducted by balsam with the same refractive index. (Fig. 4) This method fills the surface relief created while developing the amplitude modulation type HDG and thereafter the HDG acts as a pure refractive index modulated phase type grating. This helps lowering the noise level of the spectrum obtained by it.

Characteristics of a GRISM based on a HDG
processed with Br 2 Normally, a phase type HDG gained by processing a silver halide emulsion with Br 2 has little printout effect caused by external ultraviolet exposure but is very vulnerable to a humid atmosphere. [12,13] A GRISM, the type of which is the combination of the above described HDG and a prism by refractive index matching, has the important trait of being very stable in relation to external conditions.   Fig. 7 shows part of the mercury atomic spectrum obtained by the GRISM based on a HDG with the spatial frequency of 600mm -1 .
As can be seen from Fig. 7 background noise level of the spectrum is quite low and the yellow dual lines nm 0 . 577 1 = λ and nm 1 . 579 2 = λ are sufficiently separated from each other, thus enabling the GRISM to be used as a disperse unit in a direct vision spectroscope.

Conclusion
We have, based on a refractive index modulation type HDG gained by processing silver halide emulsion with Br 2 , composed a GRISM by means of refractive index matching between the HDG and a prism and investigated its characteristics. In case of a HDG with a spatial frequency of . The above experimental results show evidence that our GRISM is suitable for efficient usage as a direct-line disperse unit in a direct vision spectroscope.