The present work offers new equations for phase evaluation in measurements. Several phase-shifting equations with an arbitrary but constant phase-shift between captured intensity signs are proposed. The equations are similarly derived as the so called Carré equation. The idea is to develop a generalization of the Carré equation that is not restricted to four images. Errors and random noise in the images cannot be eliminated, but the uncertainty due to their effects can be reduced by increasing the number of observations. An experimental analysis of the errors of the technique was made, as well as a detailed analysis of errors of the measurement. The advantages of the proposed equation are its precision in the measures taken, speed of processing and the immunity to noise in signs and images.
A new time interval/frequency generator with a jitter below 5 ps is described. The time interval generation mechanism is based on a phase shifting method with the use of a precise DDS synthesizer. The output pulses are produced in a Spartan-6 FPGA device, manufactured by Xilinx in 45 nm CMOS technology. Thorough tests of the phase shifting in a selected synthesizer are performed. The time interval resolution as low as 0.3 ps is achieved. However, the final resolution is limited to 500 ps to maximize precision. The designed device can be used as a source of high precision reference time intervals or a highly stable square wave signal of frequency up to 50 MHz.