From Eqs. (30)–(38), we can gain access to an estimate of the signal complex field that exists in the exit-pupil plane of the imaging system [cf. Fig. 2 and Eq. (26)]. First, we let and and apply a 2-D inverse Fourier transformation to Eq. (34), such that Display Formula
(39)where is a sinc function. Taking a look at the remaining 2-D inverse Fourier transformation in Eq. (39), we obtain the following relationship: Display Formula
(40)where the superscript * denotes complex conjugate. From Eqs. (25) and (29), it then follows that Display Formula
(41)The first term in Eq. (41) is nothing more than a scaled 2-D autocorrelation of the desired signal complex field . This term is centered on axis and is physically twice the circumference of the exit-pupil diameter . The second term in Eq. (41) is also centered on axis and contains separable impulse functions [cf. Eq. (37)]. These impulse functions are at the strength of the uniform irradiance associated with the reference (i.e., ). The last two terms in Eq. (41) form complex conjugate pairs and contain the desired signal complex field , both scaled and shifted off axis by the coordinates .