Headphone equalization

Headphones must not be engineered to be just flat, because our external ears(& body parts) possess their own unique filtering properties:

Since headphones block our ears, they must compensate what they have taken from us. Because of their placement relative to our ears, they have spectral property similar to that of diffuse field, and most manufacturers reflect such compensation to their products. 

If you do not take the above properties into account, and design the frequency response flat like loudspeakers, the headphones would sound horrible, lacking mid-high bands. Once these filterings have been taken care of, now comes the matter of sound localization.

Since mid 80s, headphones, especially reference models from Sennheiser, AKG, Grado & Beyerdynamics, have been manufactured complying with the Diffuse-Field equalization (flat reverbrant room response w/ random incidental stereo image), thanx to G. Theile, who argued Free-Field equalization (flat anechoic response w/ a stereo image infront of the listener) colours headphones' overall spectral properties:

[with in-front localization, H(s) != H'(s)] 

In a conversation with Dr. Theile and me, he made a comment in regards to his research: 

"Our general conclusion was that physical transfer functions should be measured directly by physical methods in order to avoid psychoacoustic effects such as the SLD effect measured in the region above 100 Hz...Here the outer ear transfer function M(Ω) = 1, the probe headphone transfer function K should be flat."

And this argument had been verified once again by Japanese researchers in 1990.

 Since individual Head-Related Transfer Functions(HRTF) are all different & unique, DF curves slightly vary among different studies:

However, in 2008, Hammershøi & Møller from Denmark gathered all of the existing DF-curves(eardrum responses from 47 subjects total), and averaged into one reference curve. This is the most accurate eardrum DF response currently available:

If a tonal linearity, natural head-phonic imaging, and Hi-Fidelity are what you're looking for, search for headphones matching the above reference DF curve the most. (make sure you're comparing eardrum responses only, such as IEC-711 coupler + pinna simulator measurements & headroom, PCmag measurements) 

BTW, the most accurate DF equalized headphones in the market is ER-4 from Etymotic Research:

Red target curve references Mead Killion's study from 1987. So far, no headphones have come near close to this lil fella, when it comes down to the DF accuracy. (Maybe except Stax Lambda Pro w/ ED-1 diffuse-field EQ)

Keep in mind that the reference curve is for reference ONLY. Everyone's HRTF is slightly different from one another- you can never get a perfect flat response unless you calibrate your headphone to your own HRTF. Also, you can never achieve 'perfect flat' with headphones due to the psychoacoustic phenomenon called the missing 6dB effect unless you utilize a tactile transducer as a subwoofer. (or actually train yourself enough to compensate it)