Abstract: Under the general case of coexisting equal-inclination and equal-thickness interference in Michelson
interferometer,the generalized curve equation of interference fringes is derived rapidly and concisely using an
improved mathematical approach.Types of interference fringes are systematically categorized via discriminant
analysis.Additionally,the characteristic radial fringe density gradient( sparser center to denser periphery) in
equal-inclination patterns and micro-curvature in linear fringes of equal-thickness patterns are rigorously
demonstrated and analyzed. The new derivation method exhibits greater generality,conciseness,and
completeness,serving as a valuable reference and basis for deepening theoretical understanding of classical
physics experiments,designing innovative experimental instruments,advancing teaching reforms,and promoting
scientific research.