The accuracy of solid density primary standard is decided mainly by the accuracy of the diameter measurement of silicon sphere. With traditional five-interferogram algorithm to unwrap phase for diameter measurement, the phase steps should be equal to π/2 exactly, but this is almost impossible to achieve in nanometer positioning technique. In order to overcome this defect, we have derived an improved five-interferogram algorithm, which not only keeps the high accuracy of traditional five-inter- ferogram algorithm, but also does not require absolute equal step to unwrap phase. Instead, the improved five-interferogram algorithm only needs measuring phase shifting. Based on the improved algorithm, we have developed a novel interferometer with special etalon, and the cavity length of this etalon can be changed by pressure from vertical direction to realize phase shifting. The accuracy of this interferometer is better than 3 nm and can be improved in future research.