To assess the resolution performance of modern CT scanners, a method to measure the 3D MTF is needed. Computationally, a point object is an ideal test phantom but is difficult to apply experimentally. Recently, Thornton et al. described a method to measure the directional MTF using a sphere phantom. We tested this method for FDK reconstructions by simulating a sphere and a point object centered at (0.01 cm, 0.01 cm, 0.01 cm) and (0.01 cm, 0.01 cm, 10.01 cm) and compared the directional MTF estimated from the reconstructed sphere with that measured from an ideal point object. While the estimated MTF from the sphere centered at (0.01 cm, 0.01 cm, 0.01 cm) showed excellent agreement with that from the point object, the estimated MTF from a sphere centered at (0.01 cm, 0.01 cm, 10.01 cm) had significant errors, especially along the fz axis. We found that this is caused by the long tails of the impulse response of the FDK reconstruction far off the central plane. We developed and tested a new method to estimate the directional MTF using the sphere data. The new method showed excellent agreement with the MTF from an ideal point object. Caution should be used when applying the original method in cases where the impulse response may be wide.