Patent ID: 7944467

Claim:
A task-based imaging system for obtaining data regarding a scene for use in a task, comprising: at least one optical element for (a) imaging a wavefront of electromagnetic energy from the scene to an intermediate image and (b) modifying phase of the wavefront; and a first detector for detecting the intermediate image over a range of spatial frequencies, the at least one optical element being configured for cooperating with the first detector so that signal-to-noise ratio (SNR) of the task-based imaging system is greater than SNR of the task-based imaging system without phase modification of the wavefront over the range of spatial frequencies, wherein modifying phase is characterized by a pupil function of a form: ϕ ⁡ ( x , y ) = ∑ i , j = 0 N ⁢ ⁢ x i ⁢ α ⁡ ( i , j ) ⁢ y j , where x and y are normalized spatial coordinates, r is a radius of an entrance pupil and α(i,j) are pupil function coefficients for indices i and j with ∑ i , j = 1 N ⁢ ⁢  α ⁡ ( i , j ) ⁢ r - i - j  2 < ∑ l = 0 N ⁢ ⁢  α ⁡ ( l , 0 ) ⁢ r - l  2 +  α ⁡ ( 0 , l ) ⁢ r - l  2 , and wherein at least one of coefficients α(i,j) has a value of at least one when at least one of indices i and j equals zero.