We describe the optical characterisation of two silicon cold-electron bolometers each consisting of a small ($32 times 14~mathrm{mu m}$) island of degenerately doped silicon with superconducting aluminium contacts. Radiation is coupled into the silicon absorber with a twin-slot antenna designed to couple to 160-GHz radiation through a silicon lens.The first device has a highly doped silicon absorber, the second has a highly doped strained-silicon absorber.Using a novel method of cross-correlating the outputs from two parallel amplifiers, we measure noise-equivalent powers of $3.0 times 10^{-16}$ and $6.6 times 10^{-17}~mathrm{W,Hz^{-1/2}}$ for the control and strained device, respectively, when observing radiation from a 77-K source. In the case of the strained device, the noise-equivalent power is limited by the photon noise.