Design criteria for a single solenoid and its correction coils for the use in spin echo spectrometers are given. A single helical coil does not satisfy the requirement for very high homogeneity of the path integrals of the modulus of the magnetic field even after introduction of optimized correction coils. However, a construction of four concentric helical coils wound in different senses allows for virtually complete correction of all errors due to radial extension and divergency of the neutron beam with three "Fresnel-coil"-type correction coils. © 1990.