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Laser shearing interferometers (LSIs) are suitable for measuring the plasma-density profile on the condition that the spatial-frequency shift of the interference fringes induced by the plasma is less than the spatial-carrier frequency of the fringes. When it is applied to the diagnostics of plasmas with very large density gradient and Laplacian, such as a plasma shell produced by Z-pinch, the fringe pattern obtained in the experiment seldom meets the requirement. A new type of laser differential interferometer has been developed on the basis of a cyclic LSI. By placing a ring interferometer between the two lenses of a 4-f imaging system, the interferometer has the ability to change the ratio of frequency shift to carrier frequency arbitrarily, and thus, it is applicable to the diagnostics of plasma with large density gradient and Laplacian. The principle of the 4-f differential interferometer was illustrated. Gas-puff experiments were conducted on a Yang accelerator. The high-definition interferograms of the imploding plasma shell were obtained. The electron-density profiles and the plasma-shell shape were calculated from the interferograms.