A-1. Training purpose:

A-2 Equipment:

a: nonlinear phase modulation pseudocolorimeter, (made in Dalian maritime university) b: dark room with processing kit (ready for use) c: Ronchi grating, d: cassette (for encoding processing without dark condition), e: transparency with gray levels distribution (to be pseudo color processing) f: H-D curve (for reference).

A-3 Principle (only for lower class students)⁶

Using the characteristic curve of the holographic emulsion as shown in FIG.1. There are three portions, i.e. straight-line region, nonlinear region including gross fog region and saturation region. After developing and bleaching process, different photographic density will produce different relief thicknesses d where d is proportional to the photographic density D, and can be represented in a simple relation

the relief thickness will change the phase quantity of the incident light wave, which is referred to as the phase modulation. Two methods to be used, they are toe modulation and shoulder modulation. As for toe modulation, a fresh film or plate is used for light exposure with the log E at toe point, after that, reserve the latent image without developing ready for the next exposure. As for the shoulder modulation which is exposure closed contact with a Ronchi grating by appropriate exposure time. Both are called latent image firms or plates.

FIG. 1

Toe and shoulder point on H-D curve

When a transparency is ready for pseudo color processing, take the latent image film or plate, put it to superimpose on the transparency. If the toe modulation film or plate is used, a Ronchi grating should be used to press on the transparency in order to protect the latent image part without secondary exposure, and let the light pass through the transparent part of the grating in order to receive secondary exposure. If the shoulder modulation film or plate is used, grating is not necessary. The exposures in both cases are falling onto the linear region of the H-D curve. After developing and bleaching processing, the thickness difference produced by the latent image and that of the secondary exposure region is called effective thickness which may be denoted by the expression as

j = a(for toe modulation), j = b (for shoulder modulation). Since they are all used the nonlinear region of the H-D curve, so it is called nonlinear phase modulation. The relief corresponding to the latent image is produced only by the first exposure, so it is independent of the secondary exposure, and remains constant. During the period of secondary exposure, passing through the different gray parts of the transparency, the exposures are different due to different part of the linear region of the H_D curve. So they have different effective thickness. It should be noted that different gray levels on the transparency transferred into different effective thickness which produce different phase variations of the incident light wave…

Next, how to let the transparency of gray distribution transfer into color picture? The action of the grating ihas now been taken place. Using the principle of the diffraction of the white-lght. The relief grating is made by the simultaneously expose to the white light as shown in FIG.2 (for toe modulation)and FIG.3 (for shoulder modulation) □ Since the relief thickness whatever toe modulation or shoulder modulation remains constant, only the correspond to the different part of linear region of H_D curve can have different heights of the effective thickness to form a different phase grating. with different heights.. Using different height of phase grating to produce different colors by diffraction principle. Hence a color spectrum will be formed on the spatial frequency plane.□

FIG. 2

Rectangular model for toe modulation

FIG. 3

Rectangular model for shoulder modulation

To resolve the white light of incidence by an encoding transparency with phase modulation, a typical equipment called 4F-system may be used as shown in FIG.4. In which the encoding transparency is inserted in the input plane P₁. P₁ is illuminated by a bundle of parallel white light through a collimating lens L₁. The transmitting light fall on the focal plane of spatial frequency spectrum. through a Fourier lens L₂. constituates a color spectrum.□Such spectrum carries information of gray levels “dyed in colors.” Different gray levels dyes in different colors.

FIG. 4

4F-system of psudocolorimeter

The function of the lens L₂ is producing a diffraction pattern (or say Fourier transformation mathematically, which may be denoted by the symbol F). If the encoding relief may be described by the functionf (x, y)□then the colorful spatial frequency spectrum may be described in general as the form

where p(α, β) is the function representing the colorful spatial frequency spectrum.□So we have spectra of zeroth, first, second, third, etc., orders. The longer the wavelength, the larger the deviation for a given order of spectrum.. In order to control the color of the picture, we may select any order of spectra to go through the plane by open a small hole with appropriate size. Take zeroth order, for instance, open a small hole at the central position. Then the zeroth order spectrum will pass through the hole. This operation is referred to as optical filtering.

In general, the filtering operation may be described by a filtering function H(α, β) to represent the shape of the filtering aperture. □then the light wave passes the aperture may be denoted by the function p(α, β)H(α, β).which is the information “dyed in some colors” corresponding to the original gray levels distribution. It can be seem that we can reconstruct the original image, so long as we restore the information we have just obtained to the original shape but dyed with colorful information. Thus, the transformation from a black-and-white picture to a pseudo color image has been achieved. Since the black-and-white picture should be changed to a picture with photographic density distribution, hence it is referred to as density pseudocolor encoding technique.

In order to reconstruct the original picture with pseudo colors, we may place a imaging lens behind the filtering plane as a focal plane of the lens L₃ then the colorful image corresponding to the original black-and-white transparency will appear on the output plane of the 4F-system. In other words, L₂ realized spatial frequency spectrum transformation, and on the contrary, L₃ realized the inverse transformation.□inverse Fourier transformation□denoted by F^-1□Now let (ξ, ζ) be the colorful coordinate, then the amplitude can be express as

The intensity observation is then represented by the formula shown as follows:

If we use the relief shape as shown in FIG.2m or FIG.3, illuminating with monochromatic wave, after a theoretical calculation we obtain the intensity formula as follows

where K₁ and K₂ are constants, k is wave vector 2π /λ□μ is the refractive index of the emulsion, Ad is the effective thickness of the uniform relief at (ξ, ζ.□. It should be noted that the above formulae are only applied to the case of monochromatic light. As a matter of fact, all monochromatic light passing through the filtering aperture are mixed together at output plane, and they are related to the power spectrum G(λ) of the light source Therefore, the intensity of the mixing colors should be express by the sum of various monochromatic light waves, i.e.

It should be noted that all formulae as mentioned above are only for qualitative interpretation, no concrete functions have been given. So it is only for qualitative understand by the first-and-second-year students. The quantitative analysis is beyond the requirement of the lower class student.

A-4: Experimental method (neglected)

B: NPMT training for higher level student

B-3 Principle for making positive and negative film and relief ^3,4

a: Making positive film with gray levels

Using fresh film (or plate) for step exposure by step timer. The step exposure is defined as E_s⁽ⁿ⁾ = nE₀, where E₀ is the minimum exposure, n is an integer. Then we have a series of standard positive film (or plate). The photographic density difference of any two positive gray levels is

where n and m are the step exposure called exposure index n and m respectively, and the slop of the linear region is referred to as film γ.

b: Making negative film with gray levels

Using positive film (or plate) with step gray levels as attenuator superimpose upon a fresh film (or plate). The exposure is defined as E_c⁽ⁿ⁾ = T_s⁽ⁿ⁾ E₀, where T_s⁽ⁿ⁾ is the nth transmittance of the positive gray levels. Then we have a series of negative step gray levels. with film γ’. The photographic density difference of any two levels will be

A simple relation of transmittance between positive and negative gray levels can be obtained as

c: Negative film with toe modulation:

Using negative film (or plate) processed by toe modulation, we may put m = a, where a represents exposure index at toe point, then we have photographic density difference between toe point and any point along linear region ot H-D curve shown as follows

Since E_c⁽ⁿ⁾ / E_c^(a) = (p / n)^χ, and E_c⁽ⁿ⁾ = E_c^(a) + E_c^(n-a) hence we have

where p is the exposure index at toe, and m = n - p is the exposure index difference between toe and any exposure index along linear region of H-D curve.

d: Negative film with shoulder modulation

Using negative film (or plate) processed by shoulder modulation., we may put n = b, where b represents exposure index at shoulder. point, then we have photographic density between shoulder point and any point along linear region of H-D curve, say m, shown as follows:.

Since E_c^(b) / E_c(^m = (m / b)^γ, then we have a simple relation

C-1 Training purpose:

C-2 Equipment:

a: The same as shown in B-2, b: Color controller. c: Computer (or special microprocesser)

C-3 Principle for pseudocolor analysis:^5,7

The approximate theory called rectangular model in A-3 has been briefly introduced before. This theory may be used for qualitative interpretation how to make pseudo color picture from a black-and-white transparency. This model is not able to give exactly the chromaticity coordinates. Some references should be read by the student himself because of the requirement of independent work.. The method for computing chromaticity coordinates of pseudo colors may be referred to the papers shown behind. The duty of a tutor or a professor is that guides the student to catch knowledge by his own brain and do not take on what ought to be done by studentt. So we ‘d like say no more about it..

C-4: Experimental method (neglected).