1. Optical Requirements for Orbital
Surveillance
September 24, 2014
EGR 101.19
Room 207
William E. Lewis III
Derek Griesheim
Stephen J. Iurassich
William M. Vaughn
Sumbited to:
Dr. Matthew A. Verleger

2. Abstract
The objective is to design a low earth orbit satellite. With de-
signing a satellite it is imperative to take the proper steps in order
to complete it properly. Along with taking proper steps it is im-
portant to have maximum efficiency in every step. However various
constraints and requirements make the design task difficult. To begin
with a charge coupling device (CCD) must be selected that is both
cost efficient and high powered. The Kodak KAF 8300 is the perfect
combination of these two qualities. Excelling in both cost efficiency
and optical power. Moreover, a mirror must be configured to fit the
satellite and more importantly the charge coupling device. The mir-
ror has to fit inside the required space envelope and simultaneously be
large enough to carry the large optical abilities demanded by the CCD.
In order to accomplish this calculations have to be made. However the
consideration of cost must be put into the picture because depending
on the selection of glass can fluctuate the cost. Furthermore, power is
needed in order for the whole system to work. Photovoltaic cells are
the chosen path to power the system. Solar panels containing photo-
voltaic cells will be needed in great abundance. While cost of these
cells are rather fixed the efficiency of the power system is not. The
use of the satellite functioning at both day and night is inefficient.
Minimizing power use at night can save power along with lowering
the cost. In order to store the power batteries must be integrated
into the circuit. The batteries must be capable of storing power to
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3. run the satellite at night and will be charged during the day. Overall
the system should be able to take high resolution pictures that can be
used for security purposes.
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4. Nomenclature
a = mirror radius
Am = mirror area
b = mirror depth
D = CCD diagonal
f = focal length
h = characteristic linear dimension of object
H p = number of pixels horizontal
H w = CCD width
h = corresponding image object size
M = magnification
M ci = material cost index per unit volume
n = glass index of refraction
p = object distance
PM = CCD optical power
Pm = mirror optical power
P = pixel size
q = image distance
R = sampling resolution
rm = mirror radius
ρ = mirror density
R = optical Resolution (rad)
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5. Scp = surfacing cost Parameter
t = mirror thickness
V h = CCD height
V p = number of pixels verticle
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6. 1 Introduction
The satellite is designed for security applications while in low earth orbit.
The objective is to be able to take high resolution pictures. However, this
particular satellite is designed to be a spy satellite, therefore taking higher
resolution pictures than normally taken. In order to do this a charge coupling
device must be selected, a mirror designed and modified to fit the charge
coupling device’s specifications, and an electrical system designed to fit the
power demands of the optical system.The satellite is designed for taking
pictures with exceptional quality along with integrating technology that is
both cost efficient and superior. The satellite will be powered by photovoltaic
cells therefore giving it the ability to run on renewable energy. This, joined
by a battery, gives the satellite the capability of running continuously. The
design constraints and requirements for the satellite include: obtaining a
orbital height between 100 and 200 nautical miles, having the object linear
dimension(minimum size of the picture) be above 750 meters, the satellite
resolution less than 2.5 meters, have the mirror be able to handle the optical
power restraints of the charge coupling device (CCD), the space envelope
being a 10 foot (3.05 meters) cylinder with a 6 foot (1.83 meters) diameter.
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7. 2 Analysis
2.1 Mirror Analysis
In order to build the spherical mirror necessary to obtain adequate pho-
tographs for security applications it is necessary to start by assuming some
values. All the measurements are calculated using the metric system. The
orbital height of the satellite must be between 100 and 200 nautical miles. To
facilitate the calculations and have a better image being closer to the Earth,
the chosen height, that is also the object distance p, is 200km, a distance
within 100 and 120 nautical miles.
1 nautical mile = 1.852km
100 × 1.852km < 200km < 200 × 1.852km (1)
The mirror sector dimensions a and b are assumed values. a must not
be greater than the half of 1.83 meters which is the diameter of the cylinder
which contains the satellite. With the assumed a and b values it is possible
to calculate the surface area of the mirror and then the radius of the mirror.
Am = π × (a2
+ b2
) = π × (0.92
m + 0.452
m) = 3.1809m (2)
rm =
Am
2
× π × b = 3.1809m2
/2 = 0.5625m (3)
Knowing the radius it is possible to calculate the focal length f that is also
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8. assumed to be equal to the image distance q because of the great distance
from the Earth.
f = q =
rm
2
=
1.1250
2
m = 0.5625m (4)
The magnification M that the mirror is able to provide is determined by
the quotient between the image distance and the object distance. The same
quotient can be obtained by dividing the corresponding size of the object
in the image h and the characteristic linear dimension of an object being
imaged, h. The value of h is known to be equal to 750m. the value of h is
unknown but can be obtained by the proportion q
p
= h
h
.
M =
q
p
=
0.5625m
200000m
= 2.8125 × 10−6
(5)
After calculating the information about the shape of the spherical mirror
and the magnification, it is necessary to chose a particular type of glass
with the adequate compromise between characteristic properties and price
in USD. The characteristics to look at are: the glass index of refraction, the
mass density, the material cost index per unit volume and the surfacing cost
parameter. The glass type chosen is BK7 because it resulted in having the
best compromise between physical characteristics and cost compared to other
types of glass.
Chosen the glass type it is possible to calculate the thickness of the spher-
ical mirror, its weight and the cost.
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9. t = (0.0951×a×ρ)×10−4
= (0.0951×0.9m×2510kg/m3
)×10−4
= 0.0215m
(6)
W = 9.81×(ρ×Am×t) = 9.81×(2510kg/m3
×3.1809m2
×0.0215m) = 1.6826×103
(7)
CostUSD = Mci × Am × t +
110
n
× Scp × Am
= $1.00/cm3
× 318.09cm2
× 0.0215m + $2.40/cm2
× 318.09cm2
= $552.53
(8)
2.2 Electrical Analysis
After choosing the Kodak KAF-8300 Image Sensor the power of the CCD had
to be calculated which can be represented by the formula
Vpix × Hpix × P 3)/15000, which can be found to equal 2.44 watts. Along
with this the Command/Date Control System uses 4 watts when not in use
and 10 watts when image processing, the communication system when trans-
mitting data uses 3 watts, and the image processing system when in use uses
4 watts. Since the CCD will only be used during daytime the total needed
watts is 19.44 watts and during night time use is 7 watts.
While revolving around the earth at an orbital period of 1.47 hours or,
assuming that half of that time is spent in darkness, the total time period
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10. spent in sunlight needed to capture energy the adequate amount of energy is
0.73 hours 1.47
2
or 2650.5 seconds. Knowing that the solar cells must spend
at least 0.73 hours in sunlight per rotation, the total needed energy during
the day can be calculated to 51525.72J by multiplying 19.44 by the number
of seconds spent in sunlight, 2650.5 seconds. The total needed energy during
the night can be calculated a similar way, by taking the total number of night
time watts, 7, and multiply it by the number of seconds spent in the dark,
also 2650.5 seconds, can be calculated out to be 18553.5J.
The numbers presented in the following paragraph can be used to de-
termine the amount of energy needed in the batteries to sustain night time
function and the needed amount of energy to be captured during the day
to run the systems and charge the batteries . In order to calculate this, the
formula Enight ×1.2 (20% Error) would be appropriate, after plugging in val-
ues it can be determined that the total battery energy need is 22264.2J. For
daytime use with the solar cells, the formula (Ebat
0.6
+ Eday)/0.7 can be used
to get the figure 126618J.
Solar cells must be added connected in series and therefore their voltage
is a sum, stating that the total cells per series can be calculated 6 volts/0.5
volts to 12 cells per series. Assuming that each in-house solar cell has an
output of 0.5 volts and a maximum current of 0.080 amperes, (0.5v×0.080
amperes) the total power output per solar cell is 0.40 watts. Taking the
calculation of 12 cells per series and multiplying the total output per solar
cell (0.40 watts) will result in the total power output per series(0.48 watts).
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11. Now knowing the total output series the total output power of the solar
arrays can be determined to be Psol = Esol/Tcharge = 47.77 watts. By taking
the total output by the solar arrays and dividing it by the output per single
solar cell (47.77/0.40) it can be determined that roughly 1200 solar cells are
needed. Referring back to the calculation earlier that stated 12 cells per
series is needed, it can be determined that 100 series made up of 12 cells per
series will work adequately for this circuit.
As for the battery array they can also be placed in a series-parallel ar-
rangement like the solar cells, using the formula (6 volts/ 1.2 volts) the
solution becomes clear that 5 batteries per series is need. Each battery is
rated at 1.2 volts and can supply 0.2 amps of current for up to 12 hours,
by using the formula (P=IV) it is determined that each battery has a power
output of 0.24 watts for 12 hours or 2.88 watt-hours. The total energy in
joules per battery can be determined by using the formula (1.2 volts × 0.2
amps × 12 hours × 3600 seconds/hr) to get a solution of 10368 J/battery.
By taking the value, 22264.2 J, the total needed battery energy to sustain
power throughout the night and dividing it by the energy per battery it can
be determined that (22264.2/10368) 3 batteries are needed to sustain power
throughout the night.
2.3 CCD Analysis
In order to achieve the greatest results from the optical system a charge
coupling device (CCD) had to be selected outside of the given options. The
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12. Table 1: CCD Data
Variable Value Variable Value
Hpix 3358 Vpix 2536
P 5.4µm HCCD 17.96mm
VCCD 13.52mm DCCD 22.5mm
PCCD 2.44W PM 2.53nW
Cost $800
Kodak KAF 8300 is the selected CCD that has the desired capabilities for
optimum results. This specific design was chosen because it has qualities
that are far superior to the given options. The specifications of the charge
coupling device are given in Table 1.
With the CCD selected the optical power required by the mirror must be
compared to the optical power of the CCD. The power of the mirror must
be equal to or greater than the power required by the CCD.
Calculation for optical power needed for the charge coupling device:
PM =
5(DDR)2
(MDR)(OS)
6.241 × 1018
(9)
By doing this calculation it becomes known that the optical power re-
quired by the CCD is a lesser value than the mirror can output. This is
important because if it were the inverse situation the result image would be
black.
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13. 2.4 Magnification
With taking pictures from a distance of 100 plus nautical miles it is imper-
ative that the magnification has a high sampling resolution but at the same
time does not have too many pixels. The result of these values clashing would
be a slow transmission from satellite to earth. In order to ensure that it is
proper values the Nyquist Criterion is used.
3P ≤ MR ≤ 6P (10)
P = Image Distance
where:
M = Magnification
R = Sampling Resolution
Magnification can be found by:
M =
−q
p
(11)
where:
q = Image Distance
p = Object Dimmension
When inserting numbers into variables the resultant comes to be that
the magnification is well over the recommended value. This would cause the
satellite to transmit data much slower. However this is acceptable because it
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14. is designed to be a spy satellite. With designing a spy satellite the sampling
resolution is much higher. The satellite has the capability of taking a picture
of something 6 centimeters in size. This value is that sampling resolution.
Sampling resolution can be calculated by:
R = p ×
115.8
2a
/60 (12)
where:
a = radius of the mirror
The calculation of sampling resolution enables us to determine the size of
image at can be captured. This is important because a constraint from the
task is to have a sampling resolution of less than 2.5 meters. With a sampling
resolution of 0.06 meters this can measure the quality of the optical system
on the satellite. With a number far less that the required specification it
justifies why the sampling resolution is much higher than the recommended
value according to the Nyquist Criterion.
3 Cost Analysis
3.1 Optical Components
Using the materials given in the book, the group decided that BK7 would
have the fit for our satellite due to its lightweight, low cost of price, and qual-
ity index of refraction. Other options for our mirror materials differed from
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15. SF11 to Sapphire. While SF11 has a higher index of refraction, the weight is
a major drawback. As for Sapphire, it does offer a closely comparable index
of refraction but at almost double the price of SF11. Overall, BK7 was the
best for the price offering a cost effective component along with lightness.
3.2 Electrical Components
Using the given dollar values provided, assuming that a single 2cm x 4cm x
0.3cm solar cell costs $50.00 each and that 1200 solar cells are needed to run
the system, a cost of $60,000 is needed. As for the batteries with a cost $15
per batteries for 5 batteries the cost is $75. Adding up those values the total
cost of the electrical system is $60,075.
3.3 CCD
To be most cost efficient a CCD outside of the given CCDs had to be se-
lected. The cost of the Kodak KAF 8300 is roughly $900. Found from the
Kodak specifications on the KAF 8300 PDF document. Also the components
mounting the CCD will increase the price by a marginal factor that would
cost close to $875 for the four mounting brackets holding the CCD place.
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16. Appendix
1. Mirror Drawing
2. Mirror 3D Model
3. Bracket Drawing
4. Bracket 3D Model
5. CCD Housing Drawing
6. CCD Housing 3D Model
7. Battery Drawing
8. Circuit Drawing
9. Launch Configuration Drawing
10. Deployed Configuration Drawing
11. KODAK KAF-8300 Specification Sheet
12. KODAK KAF-8300 Pricing
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17. References
[1] Embry-Riddle Aeronautical University, “Indroduction to Engineering,”
6th. Edition
[2] Kodak, “Kodak KAF-8300 Image Ssensor,” Rev. 5.4, 14 Sep. 2010
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