Aerospace and Electronic Systems Magazine February 2018 - 45

Ahmadi, Kosari, and Malaek

Figure 7.

Figure 6.

The minimum and maximum value of DD f/H based on the constraint of
altitude in sun-synchronous orbits.

f/H vs. x, GSD = 30 m.

The objective of this sizing process part is to show the effect
of PP, GSD, and the imposed constraints on it, on the DD, and f/H.
GSD ≤ 30 m 

f
x
≥
H GSD = 30 m

(7)

The size of the detectors elements which can be used in cubesats passive optical sensors has been given in Table 8.
Based on inequality (7), for each size of the available detector
elements, the values of f/H higher than the corresponding value of x
will be acceptable, and the graph shown in Figure 6 could be drawn.
From the graph of Figure 6, the PRs and constraints could be
matched in the design plane only for the largest size of the detector
elements and the results are acceptable for the other sizes of the
detector elements.
As a result: f/H ≥ 4.67E − 7
In the case of contradiction between the above constraint and
the other requirements and constraints, it leads to impossibility of
allowable design area formation; the large sensor elements must
be ignored and the largest allowable size of the detector elements
must be chosen among the smaller ones.

Constraint of DP, H
According to the mission specifications and the general rule about
the operating orbit of the remote sensing satellites with passive optical payloads, the intended cubesat will be injected to a Sun synchronous orbit. The altitude of this kind of orbits is in the range of 600
Km to 800 Km. The reason of this limitations is explained in [28].

Table 8.

f/H vs. x , GSD = 30 m
x (μm)

The upper limit of this range is determined due to the inner Van
Allen radiation belt which begins from a/R = 1.1 and is equivalent
to H = 637.8 Km [29]. According to the statistical data, heights less
than 800 Km is acceptable.
The lower limit of this range is determined according to the
requirements of the remote sensing cubesat ballistic life in the sun
synchronous orbits.
Temporal resolution requirements, if any, also could be influential in determining the orbit altitude and change the intervals outlined above. Although these changes affect the results of cubesat
passive optical payload sizing calculations, they will not change
the method of calculation.
The driver f/H was calculated for all the available lenses in
two altitude limits and the results have been written in the Table 9.
The minimum and maximum values of f/H which are marked
with blue and red in Table 9 are shown in Figure 7 as a graph with
two boundary value which should be considered in final matching
diagram.

Table 9.

The F/H DD for All the Available Lenses in Two
Altitude Limits
f
(mm)

f/D

Hmin
(Km)

Hmax
(Km)

f/(Hmin)

f/(Hmax)

1.68

2.5

600

800

2.80E-09

2.10E-09

2.2

2.5

600

800

3.67E-09

2.75E-09

3.6

600

800

6.00E-09

4.50E-09

4.3

1.8

600

800

7.17E-09

5.38E-09

6.4

2.4

600

800

1.07E-08

8.00E-09

2.5

600

800

1.33E-08

1.00E-08

GSD (m)

f/H

1.40E-05

4.67E-07

10.06

2.8

600

800

1.68E-08

1.26E-08

8.40E-06

2.80E-07

600

800

2.67E-08

2.00E-08

6.00E-06

2.00E-07

2.5

600

800

4.17E-08

3.13E-08

3.18E-06

1.06E-07

600

800

5.83E-08

4.38E-08

2.00E-06

6.67E-08

2.5

600

800

8.33E-08

6.25E-08

FEBRUARY 2018

IEEE A&E SYSTEMS MAGAZINE

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine February 2018