Preliminary Project 2 Proposal
December 6, 2002
? Project Description:
The objective of this project is to design a spectrophotometer, which will measure
the color spectrum from a sample object at any wavelength. The object will be a piece of
single colored paper. The spectrophotometer will determine the color of the paper, and
display the color on a computer screen.
The block diagram 1 shows the basic setup of the system. The halogen light will be shined on the colored paper. The colored paper will reflect the light. By using the
lens, the reflected light can be aligned into a diffraction grating. Diffraction grating is
typically small about 8 to 10 cm wide. It consists of a reflecting surface on which many
thousands of narrow parallel groves have been made close together. A beam of light
directed at such a surface is diffracted in all directions at each groove. The light waves
reinforce each other in certain directions and cancel out in other directions. The direction
of diffraction is different for each wavelength. By letting the reflected light shine on the
diffraction grating, the colors of the light are separated (color spectrum).
After the colors of the light are separated, the next step is to measure how many components exist in each wavelength, which is associated with color. In order to do that,
the color spectrum must be captured and converted into binary data. A Charged Coupled
Device (CCD) is used to capture the color spectrum. CCD will convert the light source
into voltage which in turn will be converted into binary data by an analog-to-digital
converter. The digital data will then be converted to RGB values. By pressing the “Get
Color” button on the computer screen (Fig 4), the color and its RGB values will be
displayed on the screen.
Source Lens to focus the Diffraction grating light reflection
Analog to digital converter
to convert voltage to binary sequences
Result shown in the screen (RGB value and color sample)
Block diagram 1: basic setup of the system
Block diagram 1 shows the basic setup of the system. The CCD sensor is mounted onto
the circuit board (Fig 1). The core processing will be carried out on any window-based
platform, and C programming language will be used. The results can be seen on the
Fig 1: 2048 pixels CCD line scan camera circuit board with EPP interface
Fig 2: Block diagram for the CCD line scan camera circuit board.
Fig 3: Example of diffraction gratings
RGB values display
Output Color displayscreenGetColor
Fig 4: The screen will display the outputs
After the colored paper is placed in front of the first lens, when the “Get Color”
button is pushed on the screen, the color of the source object will be displayed on the
? Analytical Component:
As shown in Block diagram 1, the source object, two lenses, diffraction
grating, and CCD will be mounted on a piece of metal bar. After shining the halogen
light on the colored paper, the light travels through the lens (Fig 5) and shines on the
Fig 5: Example of the refraction of the lens
With the lens equation to be:
1/ object distance + 1/ image distance = 1 / focal length
The lenses that will be used for this project will have focal length of 4 cm. In order to
produce a real image, the object distance has to be greater than the focal length. The
following table shows a list of object distance with its corresponding image distance with
the focal length of 4 cm.
Object distance Image distance
Table 1: Object distances with their corresponding image distances
After the diffraction grating, the source light will be separated into different orders (Fig
6). The colors of the light are separated for each order except the zero order group (m =
0). The zero order contains the original light.
Fig 6: Example of the separation of colors by using diffraction grating
The diffraction grating that will be used for this project will have 1000 lines per mm and an angular separation of the maxima of 36 degrees. If there is no lens between the diffraction grating and the CCD sensor (width of the CCD is 2.8 cm), the minimum distance between CCD and the diffraction grating can be calculated:
tan ( 36 degrees ) = height of the CCD / the distance of the separation (D)
0.73 = 2.8 cm / D
? D = 3.8 cm
The distance between CCD sensor and the diffraction grating has to be greater than 3.8 cm. If the distance is less than 3.8 cm, then the separation of the maxima will be less than 2.8 cm, which will allow optical occlusion to occur. With blue, green, and red as the primary colors for this project, then the wavelength that the CCD needs to “see” ranges from 435 nm to 740 nm (Fig 7).
Fig 7: the spectrum of the colors
In order to project the light that contains wavelength from 435 nm to 740 nm to the CCD sensor with width of 2.8 cm, the exact distance between the diffraction grating and CCD sensor can be calculated by using the equations in Fig 8.
Fig 8: Multiple slits
With d = 1/ (1000 lines/mm) = 1um, and choosing m to be 1:
The angle for the wavelength () at 435 nm can be found: ?
? d*sin( ) = m * ?1
435nm? sin() = 1d
? = 25.78 degrees 1
The angle for the wavelength at 740 nm can be found by using the same equation:
? d*sin( ) = m * ?2
740nm? sin() = 2d
? = 47.73 degrees 2
y1? tan() = (Equ: 1) 1D
y2?tan() = (Equ: 2) 2D
and are the displacements from the central maxima to the maxima of blue yy21
and red lights. The difference of those two displacements has to be the height of the
y - y = 2.8 cm (Equ: 3) 21
Substitute ? and ?into equations 1 and 2: 12
y1 (25.78) = (Equ: 4) tanD
y2 (47.73) = (Equ: 5) tanD
Subtract equation 5 from equation 4:
yy12 (25.78) - (47.73) = - tantanDD
y?y?2.812 -0.6172 = = DD
4.547 cm ?D?
In order to project light with wavelength from 435 nm to 740 nm to the CCD
sensor, the distance between the CCD and the Diffraction grating has to be 4.547 cm.
Without a lens between the diffraction grating and the CCD sensor, the distance
between them has to be very precise when mounting them on the metal bar. By adding a
lens between the CCD and the diffraction grating, the lens can be used to calibrate the
amount of the light with wavelength between 435 nm to 740 nm to be projected on the
One factor that has to be considered is the CCD sensor; it might get hot under a
long period of operation. When the CCD sensor gets hot, it will generate more current,
and will cause some of the pixels to contain invalid data, also known as the dark current.
With some of pixels containing invalid data, the color that will show up on screen will be
different from the color of the source object.
The sampling rate of the CCD’s pixels has to precise in order to generate the
correct output color. Undersampling and oversampling occur when sampling the data is
either too slow or too fast. Both undersampling and oversampling will cause the output
color to be different from the color of the source object. Without all the information, the specific sampling rate cannot be determined at this point.
The location where the color reading will be performed needs to be analyzed. The location is very small (around 1 mm in circle). Therefore, a sequence of experiments must be done to give the user a precise location.
After RGB component values are found and displayed on the screen to the user, there may be the need to do color correction in order to compensate for the inability of the CRT monitor to display the same color as the object. This will allow the user to see the same color for both on the object and the color displayed on screen. Yet, the RGB
value will remain unchanged.
? Calibration of the device
The purpose of this project is to build a measurement tool measuring a RGB value
from an object. Hence, there must be a way to calibrate the tool and compare the result with standardized measurement tool. In the first step, the spectrophotometer will be calibrated using light emission from two different elements. We know that each element from the periodic table produces light in different wavelengths (figure below). Therefore, the spectrophotometer which ranges between 400 nm to 700 nm can be calibrated by using two elements, which will then produce wavelength below 500 nm and above 600 nm. In order to get this wavelength, additional tool is required and can be obtained from the RIT Physics Department.
The second step will compare the spectrophotometer result to other standardized spectrophotometer result which will be given the same input.