The net differential phase shift ${\mathrm{\Delta }}_t$ 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 φ and prism refractive index n. Retardance of $3\lambda /4$ (i.e., ${\mathrm{\Delta }}_t=270°$ ) is achieved with minimum angular sensitivity when $\phi =45°$ and $n=1.900822$ . Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of ${\mathrm{\Delta }}_t$ from $270°$ is $\le 4°$ over a wave length range of $0.55\le \lambda \le 1.1\mathrm{\mu m}$ in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick $\mathrm{Mg}{\mathrm{F}}_2$ film, ${\mathrm{\Delta }}_t=270°$ at two wavelengths: ${\lambda }_1=0.707\mathrm{\mu m}$ and ${\lambda }_2=4.129\mathrm{\mu m}$ . This coated prism has a maximum retardance error of $\approx 5°$ $\text{over}>\text{three octaves}$ (0.5 to $4.5\mathrm{\mu m}$ ) in the visible, near-, and mid-IR spectral range. Another mid-IR $3\lambda /4$ 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 $270°$ by $<0.5°$ over the $3–5\mathrm{\mu m}$ spectral range.