A parabolic trough reflector assembly comprising a) a flexible rectangular sheet having a mass distribution that provides uniform loading for said sheet when it is critically supported as a free-hanging element, and with said sheet having longitudinal and transverse dimensions that are compatible with forming, when critically supported as a free-hanging element, a free-hanging parabolic trough reflector (101; 501) characterized by i) a highly reflective concave surface whose transverse sections are, at every longitudinal location, identical parabolas, and ii) a predetermined system-specific value of longitudinal length, L, with said longitudinal length being measured horizontally between two unsupported edges of said parabolic trough reflector (101; 501), and iii) a predetermined system-specific value of transverse width, W, with said transverse width being measured horizontally between two supported edges of said parabolic trough reflector, and iv) a predetermined system-specific value of focal length, F; b) support fixtures which secure, hold, and critically support two opposing longitudinal edges of said sheet, wherein said sheet is critically supported as a free-hanging element, with said support fixtures establishing and maintaining the relative orientation and position of the two supported edges of said sheet so that said supported edges are parallel to each other and in the same horizontal plane, and with said support fixtures having a horizontal spacing that is equal to W, the predetermined system-specific value of transverse width of the aforementioned parabolic trough reflector (101; 501), and with said support fixtures holding and securing said supported edges of said sheet in such a manner that the edge slope at one supported edge of said sheet is +W/4F and the edge slope at the other supported edge of said sheet is -W/4F, where W and F, respectively, are the predetermined system-specific values of transverse width and focal length of the aforementioned parabolic trough reflector. a) a flexible rectangular sheet having a mass distribution that provides uniform loading for said sheet when it is critically supported as a free-hanging element, and with said sheet having longitudinal and transverse dimensions that are compatible with forming, when critically supported as a free-hanging element, a free-hanging parabolic trough reflector (101; 501) characterized by i) a highly reflective concave surface whose transverse sections are, at every longitudinal location, identical parabolas, and ii) a predetermined system-specific value of longitudinal length, L, with said longitudinal length being measured horizontally between two unsupported edges of said parabolic trough reflector (101; 501), and iii) a predetermined system-specific value of transverse width, W, with said transverse width being measured horizontally between two supported edges of said parabolic trough reflector, and iv) a predetermined system-specific value of focal length, F; i) a highly reflective concave surface whose transverse sections are, at every longitudinal location, identical parabolas, and ii) a predetermined system-specific value of longitudinal length, L, with said longitudinal length being measured horizontally between two unsupported edges of said parabolic trough reflector (101; 501), and iii) a predetermined system-specific value of transverse width, W, with said transverse width being measured horizontally between two supported edges of said parabolic trough reflector, and iv) a predetermined system-specific value of focal length, F; b) support fixtures which secure, hold, and critically support two opposing longitudinal edges of said sheet, wherein said sheet is critically supported as a free-hanging element, with said support fixtures establishing and maintaining the relative orientation and position of the two supported edges of said sheet so that said supported edges are parallel to each other and in the same horizontal plane, and with said support fixtures having a horizontal spacing that is equal to W, the predetermined system-specific value of transverse width of the aforementioned parabolic trough reflector (101; 501), and with said support fixtures holding and securing said supported edges of said sheet in such a manner that the edge slope at one supported edge of said sheet is +W/4F and the edge slope at the other supported edge of said sheet is -W/4F, where W and F, respectively, are the predetermined system-specific values of transverse width and focal length of the aforementioned parabolic trough reflector.