# How to transform flat-field corrected spectra to those under Standard illuminant E (ideal equal energy illuminant)

My ultimate goal is to convert a flat-field corrected hyperspectral image of reflectance (360nm-780nm) to corresponding CIEXYZ image and thus device-independent color image.

By flat-field correction, I meant

$$I_{corrected} = {{I_{raw}-I_{black}}\over{I_{99\%white}-I_{black}}}$$

Even after the flat-field correction, it was found that the spectra still did not match published values (of a color target) under standard illuminant E. Currently, we scale and shift the intensity values for each wavelength based on published spectra to match values between measured and published CIEXYZ. Resulting average Delta E (CIEDE2000) is about 1.00.

But I wonder if there is any better way.