The invention generally relates to methods for determining a concentration of at least one target analyte in a heterogeneous sample and methods for detecting a condition. In certain aspects, the inventions provides methods that involve illuminating a heterogeneous sample, such as a biological sample, including at least one target analyte with polychromatic light, receiving luminous data of the heterogeneous sample and the at least one target analyte with a detector without splitting the polychromatic light into individual wavelengths and generating spectral data therefrom. The spectral data is then converted into a concentration of the at least one target analyte in the biological sample by comparing the spectral data to a database comprising known spectra already associated with concentration levels.

A spectrometer employs multiple filters having complex filter spectra that can be generated robustly from received light over short optical path lengths. The complex filter spectra provide data that can be converted to a spectrum of the received light using compressed sensing techniques. The result is a more compact, easily manufactured spectrometer.

A method for illumination of an object to be observed to be observed and the background, the method comprising the steps of: obtaining a relationship between wavelength and spectral radiance of the object while the object and the background are illuminated by a first light source that emits light that has a continuous spectrum in the wavelength range from 380 nanometers and 780 nanometers, and determining a value of representative wavelength that corresponds to a maximum value of the spectral radiance of the object plotted against wavelength or values of representative wavelength that correspond to maximum values of the spectral radiance of the object plotted against wavelength; determining a value or values of comparative wavelength; and illuminating the object and the background with light of the value or values of representative wavelength and light of the value or values of comparative wavelength.

A method for illumination of an object to be observed to be observed and the background, the method comprising the steps of: obtaining a relationship between wavelength and spectral radiance of the object while the object and the background are illuminated by a first light source that emits light that has a continuous spectrum in the wavelength range from 380 nanometers and 780 nanometers, and determining a value of representative wavelength that corresponds to a maximum value of the spectral radiance of the object plotted against wavelength or values of representative wavelength that correspond to maximum values of the spectral radiance of the object plotted against wavelength; determining a value or values of comparative wavelength; and illuminating the object and the background with light of the value or values of representative wavelength and light of the value or values of comparative wavelength.