Generalizing the confocal microscope via heterodyne interferometry and digital filtering

SUMMARY We describe a generalized confocal optical microscope which measures both phase and amplitude, separately and simultaneously. The system is based on heterodyne inferometry, and is extremely fast and accurate. Together with the associated signal processing and data acquisition system, it can take data at the rate of 50,000 points/s, to an accuracy of 12 bits in amplitude and about the same in phase. The 1s̀ phase error is 01°, corresponding to a height uncertainty of 0.1 nm. Unlike most phase‐sensitive systems of this accuracy, the phase data are not differential, and we are not restricted to small phase changes. Having phase and amplitude enables use of digital filters to modify the coherent transfer function of the microscope in almost any way we desire (within the bandwidth available), and in particular to double the spatial resolution of the system without resorting to ultraviolet light or ad hoc image processing procedures such as non‐linear transformations or the introduction of additional assumptions about the sample. In contrast to ordinary apodizing schemes involving annular pupils and graded neutral‐density filters, the digital filters used here are very easily changed to optimize the trade‐off of resolution versus ringing. Computationally efficient expressions for the line‐spread function and step response of a confocal microscope are developed for use in comparisons.