Problems stemming from quantitative phase imaging from intensity measurements play a key role in many fields of physics. Techniques based on the transport of intensity equation require an estimate of the axial derivative of the intensity to invert the problem. Derivation formulas in two adjacent planes are commonly used to experimentally compute the derivative of the irradiance. Here we propose a formula that improves the estimate of the derivative by using a higher number of planes and taking the noisy nature of the measurements into account. We also establish an upper and lower limit for the estimate error and provide the distance between planes that optimizes the estimate of the derivative.
© 2007 Optical Society of America
Original Manuscript: July 19, 2007
Manuscript Accepted: August 29, 2007
Published: November 12, 2007
Marcos Soto and Eva Acosta, "Improved phase imaging from intensity measurements in multiple planes," Appl. Opt. 46, 7978-7981 (2007)