The net differential phase shift Delta(t) introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence phi and prism refractive index n. Retardance of 3lambda/4 (i.e., Delta(t)=270 degrees) is achieved with minimum angular sensitivity when phi=45 degrees and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Delta(t) from 270 degrees is < or = 4 degrees over a wavelength range of 0.55 < or = lambda < or = 1.1 microm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF(2) film, Delta(t)=270 degrees at two wavelengths: lambda(1)=0.707 microm and lambda(2)=4.129 microm. This coated prism has a maximum retardance error of approximately 5 degrees over > three octaves (0.5 to 4.5 microm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3lambda/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270 degrees by < 0.5 degrees over the 3-5 microm spectral range.