**Exhibit 10.4**

August 10, 2010 

Dr. Kent A. Murphy, Ph.D. 

c/o LunaInnovations Incorporated 

1 Riverside Circle, Suite 400 

Roanoke, VA 24016 

Dear Kent: 

Reference is made to that certain Amended and Restated Investor Rights Agreement, dated as of January 13, 2010 (the“***Rights Agreement***”), by and among Luna Innovations Incorporated, a Delaware corporation (the “***Company***”), Carilion Clinic and certain other stockholders of the Company, including you. The purpose ofthis side letter agreement (this “***Letter Agreement***”) is to confirm our mutual agreement and understanding with respect to your registration rights under the Rights Agreement following the cessation of your role as the ChiefExecutive Officer of the Company. Specifically, the Company and you (hereinafter, “***Dr. Murphy***”) agree as follows: 

**1.**All capitalized terms not defined in this Letter Agreement shall have the respective meanings ascribed to them in the Rights Agreement.

**2.**This Letter Agreement is effective as of the date hereof. 

**3.**Beginning the date hereof, and through the period ending at the close of business on December 31, 2011 (the “***Restricted Period***”), Dr. Murphy hereby agrees thathe shall not (a) make any permitted transfers of Registrable Securities in accordance with Rule 144 under the Securities Act as otherwise permitted under Section 2.8(b) of the Rights Agreement, (b) exercise any of his rights as an“Initiating Holder” under Section 2.1 of the Rights Agreement or (c) exercise any of his rights as a “Holder” under Section 2.1 or 2.3 of the Rights Agreement; provided, however, that Dr. Murphymay request one Form S-3 registration pursuant to, and in accordance with, Section 2.3 and other relevant provisions of the Rights Agreement during the Restricted Period for the registration of up to 800,000 shares of Common Stock (the“***Eligible Shares***”) then held by Dr. Murphy (such registration the “***Special Registration***”). For the avoidance of doubt, the parties acknowledge and agree that a Special Registration may include a“shelf” registration on Form S-3 relating to the offer and sale of all or any portion of the Eligible Shares from time to time pursuant to Rule 415 under the Securities Act. 

**4.**If Dr. Murphy requests the Special Registration, Dr. Murphy may not transfer any Registrable Securities pursuant to the registration statement (the “***Special RegistrationStatement***”) filed in connection with the Special Registration if, in the Company’s good faith and reasonable judgment, such disposition by Dr. Murphy would be reasonably likely to jeopardize the Company’s eligibility toreceive award funding under the U.S. Small Business Administration’s Small Business Innovation Research (SBIR) program, as set forth in 13 C.F.R. 121 as in effect from time to time; provided, however, that this limitation shallcease to apply if the Company ceases to be eligible to receive award funding under the SBIR program for any reason other than as a result of actions taken by Dr. Murphy. The plan of distribution section of the Special Registration Statementshall describe the limitations on transfer set forth in this paragraph 4. 

 

**5.**During the RestrictedPeriod, if Dr. Murphy desires or proposes to make any non-registered sale, assignment, transfer or other disposition to any natural person who is a U.S. citizen of all or any portion of his Restricted Securities, or any beneficial interesttherein (e.g., pursuant to Section 2.8(a)(ii) of the Rights Agreement), the Company hereby agrees to (a) use its commercially reasonable efforts to cooperate in providing information reasonably requested by the proposed transferee inconnection with his or her due diligence investigation of the Company and (b) not unreasonably object to the proposed transfer; provided, however, that if the Company shall cease to be eligible to receive award funding under theSBIR program for any reason other than as a result of actions taken by Dr. Murphy, the Company’s obligations under this paragraph 5 shall extend to any other transferee the proposed transfer to whom would be permissible underSection 2.8(a)(ii) of the Rights Agreement, so long as Dr. Murphy has complied with the provisions of that section. 

**6.**Notwithstanding anything in the Rights Agreement or herein, Dr. Murphy hereby agrees that he will not, without the consent of the Company, take any action intended or reasonably likely to cause any Registrable Securities to be transferredto (X) any current or potential competitor of the Company or (Y) any party Dr. Murphy actually knows is intending to effect a Change of Control of the Company. 

**7.**The parties hereto acknowledge their mutual understanding that Section 3.14 of the Rights Agreement is not intended to permit the Company to alter the contractual rights of Dr. Murphyunder the Rights Agreement, as modified by this Letter Agreement, by amendment of the Company’s Bylaws or its Amended and Restated Certificate of Incorporation. Without limiting the foregoing sentence, Dr. Murphy and the Company agree toact in good faith not to circumvent or otherwise frustrate the purpose and intent of this Letter Agreement. 

**8.**Other than as set forthin this Letter Agreement, all of the terms and conditions of the Rights Agreement are and shall continue in full force and effect. This Letter Agreement and the Rights Agreement collectively constitute the entire understanding of the parties withrespect to the subject matter hereof and thereof and supersede any prior understanding, oral or written, between or among the parties (including the Second Amended and Restated Stock Sale Restriction Agreement dated as of February 27, 2008 byand between the Company and Dr. Murphy) with respect thereto. To the extent there is a conflict between the terms of this Letter Agreement and the terms of the Rights Agreement, this Letter Agreement shall control. 

**9.**Each party hereto agrees to execute and deliver, by the proper exercise of its entity or individual powers, all such other and additionalinstruments and documents and do all such other acts and things as may be necessary to more fully effectuate this Letter Agreement. 

 

**10.**This Letter Agreement maybe executed in two or more counterparts, each of which will be deemed an original, but all of which together will constitute one and the same instrument. 

**11.**This Letter Agreement may be modified or amended only by a writing signed by each party hereto and may be waived only in a writing signed by the party or parties making such waiver. 

**12.**This Letter Agreement shall be governed by and construed in accordance with the internal, substantive laws of the Commonwealth of Virginia,without regard to the conflicts of laws principles thereof. 

If the foregoing accurately reflects our agreement with respectto the matters addressed above, please so indicate by signing below. 

Sincerely, 

**LUNA INNOVATIONS INCORPORATED**

 
By: 
/s/ Dale Messick
Name: Dale MessickTitle: Interim President and Chief Operating Officer
/s/ Kent A. Murphy, Ph.D.
**KENT A. MURPHY, PH.D**
**[Counterpart Signature Page to Letter Agreement]**