Changin the optical depth (axial resoltuion) on an Optical Cohernce Tomagrpahy system So the axial resolution in a OCT system is given by:
$$I_c=\frac{4ln2}{\pi}\frac{\lambda^2}{\Delta \lambda}$$
My question what would you do to say increase the axial resolution, and how would it effect the image quality?

So looking at the above diagram which kinda answer the first part of my question, that if you move the reference mirror you will either decrease on increase the axial resolution, but how dose the relate to the central wavelength and the bandwidth? 
As from the above equation, central wavelength is given by $\lambda$ and the broadband is given by $\Delta \lambda$
 A: Moving the reference mirror does not change the axial resolution. Its action is to "bring the image in focus", so to speak. Because the light has short coherence length $\Delta\lambda$, the two beams split by the beam splitter do not interfere on the detector. They show clear interference (which is the raw signal) when the optical path difference   (OPD = $\int n_{\text{index}} ds_{\text{path}}$) is less than the coherence length, and you need to move the mirror to adjust the OPD. 
In analogy, bringing an image in and out of focus is not the same thing as changing the performance (resolution) of the microscope, for the latter, you need to control the numerical aperture.
A: 
My question what would you do to say increase the axial resolution, and how would it effect the image quality?

Increased $z$ resolution can increase scanning time which prevents the acquisition of volumetric OCT images in clinical environment due to significant motion artifacts and in some cases, for example in ophthalmology, it exceeds the maximum permissible exposure limit of biological tissue.
Spectral Domain OCT (SD-OCT) systems with close to 1 µm axial resolution in biological tissue and data acquisition rates up to 70 kHz have been reported:
R. Yadav, K. S. Lee, J. P. Rolland, J. M. Zavislan, J. V. Aquavella, and G. Yoon, “Micrometer axial resolution OCT for corneal imaging”, Biomed. Opt. Express 2(11), 3037–3046 (2011).
L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography”, Nat. Med. 17(8), 1010–1014 (2011).
R. M. Werkmeister, A. Alex, S. Kaya, A. Unterhuber, B. Hofer, J. Riedl, M. Bronhagl, M. Vietauer, D. Schmidl, T. Schmoll, G. Garhöfer, W. Drexler, R. A. Leitgeb, M. Groeschl, and L. Schmetterer, “Measurement of Tear
Film Thickness Using Ultrahigh-Resolution Optical Coherence Tomography”, Invest. Ophthalmol. Vis. Sci.
54(8), 5578–5583 (2013).
D. Cui, X. Liu, J. Zhang, X. Yu, S. Ding, Y. Luo, J. Gu, P. Shum, and L. Liu, “Dual spectrometer system with spectral compounding for 1-μm optical coherence tomography in vivo”, Opt. Lett. 39(23), 6727–6730 (2014).
C. S. Cheung, M. Spring, and H. Liang, “Ultra-high resolution Fourier domain optical coherence tomography for old master paintings”, Opt. Express 23(8), 10145–10157 (2015).
P. Tankam, Z. He, Y. J. Chu, J. Won, C. Canavesi, T. Lepine, H. B. Hindman, D. J. Topham, P. Gain, G. Thuret, and J. P. Rolland, “Assessing microstructures of the cornea with Gabor-domain optical coherence microscopy: pathway for corneal physiology and diseases”, Opt. Lett. 40(6), 1113–1116 (2015).
SD-OCT provides a significant increase in resolution over TD-OCT.

Human retinal images using (A) A spectrometer-based spectral domain optical coherence tomography (SD-OCT) System and (B) Time domain optical coherence tomography (TD-OCT) System.
NFL, nerve fiber layer; GCL, ganglion cell layer; IPL, inner plexiform layer; INL, inner nuclear layer; OPL, outer plexiform layer; ONL, outer nuclear layer; ELM, external limiting membrane; IS/OS, photoreceptor inner and outer segment junction; RPE, retinal pigment epithelium; CC, choriocapillaris.
Quantum optical coherence tomography (Q-OCT), which utilizes two-photon interference between entangled photon pairs, is a promising approach to overcome the problem with optical coherence tomography (OCT): As the resolution of OCT becomes higher, degradation of the resolution due to dispersion within the medium becomes more critical.
In the paper: "0.54 μm resolution two-photon interference with dispersion cancellation for quantum optical coherence tomography" (Dec 14 2015), by Masayuki Okano, Hwan Hong Lim, Ryo Okamoto, Norihiko Nishizawa, Sunao Kurimura and Shigeki Takeuchi, they report on the realization of 0.54μm resolution two-photon interference, which surpasses the current record resolution 0.75μm of low-coherence interference for OCT


OCT and Q-OCT schemes
(a) Schematic diagram of OCT. $I(\tau)$ is the interfered light intensity measured at a detector with varying delay $\tau$ (inset). BS is a beam splitter. (b) Schematic diagram of Q-OCT. $C(\tau)$ is the coincidence count rate counted at two single photon detectors with varying delay $\tau$ (inset).

The Q-OCT interference dip $C(\tau)$, which is so called Hong-Ou-Mandel (HOM) dip, is obtained by the coincidence count rate with varying delay $\tau$ (Fig. 1b inset). Due to the frequency correlation of entangled photon pairs, the resolution of Q-OCT (the width of the HOM dip) does not change even with group velocity dispersion (GVD) in the medium. This ‘dispersion cancellation’ of two-photon interference (TPI) was first demonstrated with 19 μm resolution and very recently with 3μm resolution, where the (GVD) effect becomes significant.

How does the bandwidth relate to resolution?

When the bandwidth of the source is made broader to achieve higher resolution, the resolution,  far from being improved, degrades due to dispersion in the medium. When a wide bandwidth signed passed through layers of differing refraction, sometimes varying based on wavelength, the group delay will not be constant across all frequencies causing a temporal smearing of the signal.
Also see: "High-order dispersion effects in two-photon interference" (Jul 20 2016), by Z. Mazzotta, S. Cialdi, D. Cipriani, S. Olivares, and M. G. A. Paris.
