Biophotonics_Concepts_to_Applications

G(x)¼U 0 asexpðasxÞ

HereΦ 0 is the incident photonflux per unit area given by

U 0 ¼

Pinð 1 RfÞ

Ahm

where A is the detector area, Rfis the surface reflectance, and hνis the

photon energy. From this, show that the primary photocurrent in the

depletion region of width w is given by Eq. (5.6).

5 :6 Consider a sinusoidally modulated optical signal P(t) of frequencyω, mod-

ulation index m, and average power P 0 given by

PtðÞ¼P 0 ðÞ 1 þm cosxt^2

Show that when this optical signal falls on a photodetector, the mean-square

signal current i^2 s

generated consists of the following sum of a dc (average)

component idcand a signal current ip

i^2 s

¼i^2 dcþ i^2 p

DE

¼ðRP 0 Þ^2 þ

1

2

ðmRP 0 Þ^2

where the responsivityRis given by Eq. (5.8).
5 :7 A given InGaAs pin photodiode has the following parameters at 1550 nm:
iD= 1.0 nA,η=0.95,RL=500Ω, and the surface leakage current is negli-
gible. Assume the incident optical power is 500 nW (−33 dBm) and the receiver
bandwidth is 150 MHz. Show that the primary current and the mean-square
noise currents are as follows: (a) ip=0.593μA; (b) i^2 shot
= 2.84× 10 −^17 A^2 ;
(c) i^2 DB
= 4.81× 10 −^20 A^2 ; (d) i^2 T
= 4.85× 10 −^15 A^2.
5 :8 A given InGaAs avalanche photodiode has a quantum efficiency of 90 % at a
wavelength of 1310 nm. Suppose 0.5μW of optical power produces a
multiplied photocurrent of 8μA. Show that the multiplication M = 16.
5 :9 A biophotonics engineer has a choice between two cameras that are based on
a CCD array or a CMOS array, respectively. Using resources from the Web
or from vendor catalogs, list some of the tradeoffs between selecting one or
the other of these instruments. Consider factors such as speed of response,
image quality, camera power consumption, camera size, and the capability to
enhance certain areas of the viewed image.
5 :10 A certain PMT has 12 dynode stages. In thefirstfive stages, each primary
electron can stimulate four secondary electrons. In the next seven dynodes,
each primary electron can stimulatefive secondary electrons. Show that the
gain of this PMT is 8× 107.

144 5 Fundamentals of Optical Detectors