Optical system comprising a diffractive optical element, and method of designing the same

An optical system comprising at least one diffractive optical element on an optical axis thereof, characterized in that:

• said diffractive optical element is a transmission blaze grating constructed of a relief having a sawtooth shape in section, said transmission blaze grating having a side wall substantially vertical to a grating surface thereof, and
• said optical system comprises said optical axis and at least one entrance surface vertical to a grating groove, wherein an angle θen of an incident light ray with a normal to said grating groove on said entrance surface and a construction of said blaze grating in a region of said grating surface on which said incident light is incident satisfies the following relationship with respect all light rays on said entrance surface upon incidence on said diffractive optical element:
• 1≧PSE×SE>0.8
• where
• PSE=|sin π(m−φ)/{π(m−φ)}|2
• φ=h/λ·(nex cos θex(m)−nen cos θen)
• nex sin θex(m)=nen sin θen+mλ/p
• SE={1−{square root}(SE12+SE22)}2
• SE1=k1·(h/p) tan θave
• SE2=k2·λ/p
• θave=(θen+θex(m))/2
• k1=0.85
• k2=0.3·|h/λ|0.35
• wherein nen is a refractive index of an entrance side medium, nex is a refractive index of an exit side medium, h is a grating groove depth, p is a grating pitch, m is an order of diffraction at which diffraction efficiency is maximized, θex(m) is an angle of an m-order diffracted light ray with the normal to the grating surface, and λ is a wavelength of light used.