Specific detectivity

Specific detectivity, or D*, for a <a href="/facts/Photodetector/7cSkXS6s">photodetector</a> is a <a href="/facts/Figure_of_merit/kdSJ3Cpy">figure of merit</a> used to characterize performance, equal to the reciprocal of <a href="/facts/Noise-equivalent_power/7KSh6FSu">noise-equivalent power</a> (NEP), normalized per square root of the sensor's area and frequency bandwidth (reciprocal of twice the integration time).
Specific detectivity is given by 
 
 
 
 
 D
 
 ∗
 
 
 =
 
 
 
 A
 Δ
 f
 
 
 N
 E
 P
 
 
 
 
 
 {\displaystyle D^{*}={\frac {\sqrt {A\Delta f}}{NEP}}}
 
, where 
 
 
 
 A
 
 
 {\displaystyle A}
 
 is the area of the photosensitive region of the detector, 
 
 
 
 Δ
 f
 
 
 {\displaystyle \Delta f}
 
 is the bandwidth, and NEP the noise equivalent power in units [W]. It is commonly expressed in Jones units (
 
 
 
 c
 m
 ⋅
 
 
 H
 z
 
 
 
 /
 
 W
 
 
 {\displaystyle cm\cdot {\sqrt {Hz}}/W}
 
) in honor of <a href="/facts/Robert_Clark_Jones/1oBkor2E">Robert Clark Jones</a> who originally defined it.
Given that noise-equivalent power can be expressed as a function of the <a href="/facts/Responsivity/8ks9YC5D">responsivity</a> 
 
 
 
 
 
 R
 
 
 
 
 {\displaystyle {\mathfrak {R}}}
 
 (in units of 
 
 
 
 A
 
 /
 
 W
 
 
 {\displaystyle A/W}
 
 or 
 
 
 
 V
 
 /
 
 W
 
 
 {\displaystyle V/W}
 
) and the <a href="/facts/Noise_spectral_density/WAGesbqr">noise spectral density</a> 
 
 
 
 
 S
 
 n
 
 
 
 
 {\displaystyle S_{n}}
 
 (in units of 
 
 
 
 A
 
 /
 
 H
 
 z
 
 1
 
 /
 
 2
 
 
 
 
 {\displaystyle A/Hz^{1/2}}
 
 or 
 
 
 
 V
 
 /
 
 H
 
 z
 
 1
 
 /
 
 2
 
 
 
 
 {\displaystyle V/Hz^{1/2}}
 
) as 
 
 
 
 N
 E
 P
 =
 
 
 
 S
 
 n
 
 
 
 R
 
 
 
 
 
 {\displaystyle NEP={\frac {S_{n}}{\mathfrak {R}}}}
 
, it is common to see the specific detectivity expressed as 
 
 
 
 
 D
 
 ∗
 
 
 =
 
 
 
 
 
 R
 
 
 ⋅
 
 
 A
 
 
 
 
 S
 
 n
 
 
 
 
 
 
 {\displaystyle D^{*}={\frac {{\mathfrak {R}}\cdot {\sqrt {A}}}{S_{n}}}}
 
.
It is often useful to express the specific detectivity in terms of relative noise levels present in the device. A common expression is given below.

D
          
            ∗
          
        
        =
        
          
            
              q
              λ
              η
            
            
              h
              c
            
          
        
        
          
            [
            
              
                
                  
                    4
                    k
                    T
                  
                  
                    
                      R
                      
                        0
                      
                    
                    A
                  
                
              
              +
              2
              
                q
                
                  2
                
              
              η
              
                Φ
                
                  b
                
              
            
            ]
          
          
            −
            1
            
              /
            
            2
          
        
      
    
    {\displaystyle D^{*}={\frac {q\lambda \eta }{hc}}\left[{\frac {4kT}{R_{0}A}}+2q^{2}\eta \Phi _{b}\right]^{-1/2}}

With q as the electronic charge, 
 
 
 
 λ
 
 
 {\displaystyle \lambda }
 
 is the wavelength of interest, h is the Planck constant, c is the speed of light, k is the Boltzmann constant, T is the temperature of the detector, 
 
 
 
 
 R
 
 0
 
 
 A
 
 
 {\displaystyle R_{0}A}
 
 is the zero-bias dynamic resistance area product (often measured experimentally, but also expressible in noise level assumptions), 
 
 
 
 η
 
 
 {\displaystyle \eta }
 
 is the quantum efficiency of the device, and 
 
 
 
 
 Φ
 
 b
 
 
 
 
 {\displaystyle \Phi _{b}}
 
 is the total flux of the source (often a blackbody) in photons/sec/cm2.

Specific detectivity open-in-new

Specific detectivity