Varied space diffraction grating and in-focus monochromator

A grating which comprises:

• a. a concave surface;
• b. a plurality of substantially parallel diffracting elements spaced from each other by unequal distances as projected upon a chord of said concave surface, according to a density function;
• c. an object point substantially fixed in space;
• d. an image point substantially fixed in space;
• e. a first path length equal to the distance which extends between said fixed object point and a first one of said diffracting element plus the distance which extends between said first diffracting element and said fixed image point;
• f. a second path length equal to the distance which extends between said fixed object point and a second one of said differacted element plus the distance which extends between said second diffracting element and said fixed image point;
• wherein the difference between said first and second path lengths plus a distance equal to a non-zero integer times a chosen wavelength times an integer equal to one plus the number of diffracting elements intervening said first and said second diffracting elements, defines a path-length error function, said grating characterized in that said concave surface, density function and said object and image points are chosen such that said path-length error function when written as a sum of powers of said chord distance between said first and said second diffracting elements lacks both second and third power terms at more than one distinct said chosen wavelength diffracted from said fixed object to said fixed image, said distinct wavelengths being determined by rotation of said grating about a fixed axis.