An optical system comprising: an optical reflecting element having a surface with an aspherical shape, the optical reflecting element having a principal axis perpendicular to the surface and intersecting the aspherical surface at a vertex thereof, the aspherical surface further being rotationally asymmetric around the principal axis; an optical source configured to emit an incident beam toward the optical reflecting element; wherein the optical reflecting element is configured to receive said incident beam, the incident beam having an incidence angle (θ inc) with respect to the aspherical surface; wherein the aspherical surface has an in-plane radius of curvature (R i) that spatially varies in an in-plane direction, the in-plane direction corresponding to a plane including the incident beam and the perpendicular to the surface at an incidence point; characterized in that the optical reflecting element has an in-plane cross section surface profile in the in-plane direction, wherein said in-plane cross section surface profile is configured to satisfy the following: the multiplication of the cosine of the incidence angle (θ inc) raised to a non-zero exponent by the in-plane radius of curvature (R i) is non-zero and is equal to 2fo with a variation less than twenty percent between any two points on the in-plane cross section surface profile, wherein the in-plane cross section of the aspherical surface profile follows one of the following second order non-linear differential equations: 2 f o y ′′ − y ′ 3 − y ′ = 0 wherein said non-zero exponent is 1, or wherein said non-zero exponent is -1, and wherein f o is a parameter controlling a focal length of the optical reflecting element; wherein the in-plane radius of curvature (R i) at each incident point is defined by ([1+y' 2] 3/2)/y", where - y' is a first derivative of y with respect to x, - y" is a second derivative of y, and - x and y are variables of an x-y orthogonal coordinate system oriented such that the incident beam is incident in parallel with respect to the x-axis. an optical reflecting element having a surface with an aspherical shape, the optical reflecting element having a principal axis perpendicular to the surface and intersecting the aspherical surface at a vertex thereof, the aspherical surface further being rotationally asymmetric around the principal axis; an optical source configured to emit an incident beam toward the optical reflecting element; wherein the optical reflecting element is configured to receive said incident beam, the incident beam having an incidence angle (θ inc) with respect to the aspherical surface; wherein the aspherical surface has an in-plane radius of curvature (R i) that spatially varies in an in-plane direction, the in-plane direction corresponding to a plane including the incident beam and the perpendicular to the surface at an incidence point; characterized in that the optical reflecting element has an in-plane cross section surface profile in the in-plane direction, wherein said in-plane cross section surface profile is configured to satisfy the following: the multiplication of the cosine of the incidence angle (θ inc) raised to a non-zero exponent by the in-plane radius of curvature (R i) is non-zero and is equal to 2fo with a variation less than twenty percent between any two points on the in-plane cross section surface profile, wherein the in-plane cross section of the aspherical surface profile follows one of the following second order non-linear differential equations: 2 f o y ′′ − y ′ 3 − y ′ = 0 wherein said non-zero exponent is 1, or wherein said non-zero exponent is -1, and wherein f o is a parameter controlling a focal length of the optical reflecting element; wherein the in-plane cross section of the aspherical surface profile follows one of the following second order non-linear differential equations: 2 f o y ′′ − y ′ 3 − y ′ = 0 wherein said non-zero exponent is 1, or wherein said non-zero exponent is -1, and wherein f o is a parameter controlling a focal length of the optical reflecting element; wherein the in-plane radius of curvature (R i) at each incident point is defined by ([1+y' 2] 3/2)/y", where - y' is a first derivative of y with respect to x, - y" is a second derivative of y, and - x and y are variables of an x-y orthogonal coordinate system oriented such that the incident beam is incident in parallel with respect to the x-axis. - y' is a first derivative of y with respect to x, - y" is a second derivative of y, and - x and y are variables of an x-y orthogonal coordinate system oriented such that the incident beam is incident in parallel with respect to the x-axis.