To solve the problems that the structure is too close to mounting the optomechanism for the engineering application, the bias slit and the thinned hemisphere lens were supplied to move enough lateral and axial air spaces between the slit, the imaging plane and the hemisphere lens. The stigmatic condition for the advanced Dyson system was obtained by the geometric optical path analysis. Another two spherical lenses were introduced between the hemisphere lens and the concave grating to eliminate extra spherical aberrations and chromatic aberrations brought by the axial air spaces. The optical system of the imaging spectrometer with small F number in a broadband was designed by the advanced Dyson spectrometer and Schwarzschild two mirrors system. An example operating in 320~1 000 nm with F number 1.8 was built. The results demonstrate that aberrations are totally corrected, the modulation transfer functions of all fields of view are larger than 0.5 in the waveband, and the spectral resolution is 3.6 nm. The proposed system can be used for the coastal ocean hyper-spectrum observation.