LUNA INNOVATIONS INCORPORATED

Exhibit 10.2

Execution Copy

THIS WARRANT AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”). THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT AS TO SUCH SECURITIES UNDER THE ACT OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED. THIS WARRANT MUST BE SURRENDERED TO THE COMPANY AS A CONDITION PRECEDENT TO THE SALE, PLEDGE, HYPOTHECATION OR OTHER TRANSFER OF ANY INTEREST IN ANY OF THE SHARES REPRESENTED BY THIS WARRANT.

LUNA INNOVATIONS INCORPORATED

WARRANT TO PURCHASE COMMON STOCK

Void After 5 P.M. Eastern Time on December 31, 2020

THIS CERTIFIES THAT, for value received, Carilion Clinic, formerly known as Carilion Health System, or assigns, with its principal office at Carilion Roanoke Memorial Hospital, First Floor, 1906 Belleview Ave., Roanoke, Virginia 24033 (the “Holder”), is entitled to subscribe for and purchase at the Exercise Price (defined below) from LUNA INNOVATIONS INCORPORATED, a Delaware corporation, with its principal office at 1 Riverside Circle, Suite 400, Roanoke, Virginia 24016 (the “Company”) up to that number of the Exercise Shares of the Common Stock, par value $0.001, of the Company (the “Common Stock”) determined in accordance with the terms of this Warrant and the attachments hereto (the “Warrant”).

1. DEFINITIONS. As used herein, the following terms shall have the following respective meanings:

(a) “Exercise Period” shall mean the period commencing at 5:00 P.M. Eastern Time on December 31, 2012 and continuing for eight (8) years thereafter.

(b) “Exercise Price” shall mean $2.50 per share, subject to adjustment pursuant to Section 5 below.

(c) “Exercise Shares” shall mean the 10,000 shares of Common Stock issuable upon exercise of this Warrant, subject to adjustment pursuant to the terms herein, including but not limited to adjustment pursuant to Section 5 below.

2. EXERCISE OF WARRANT.

2.1 Procedure. The rights represented by this Warrant may be exercised in whole or in part at any time during the Exercise Period, by delivery of the following to the Company at its address set forth above (or at such other address as it may designate by notice in writing to the Holder):

(a) An executed Notice of Exercise in the form attached hereto (the “Notice of Exercise”);

(b) Payment of the Exercise Price either (i) in cash, by wire transfer or by check, (ii) by cancellation of indebtedness, or (iii) by net exercise in accordance with Section 2.2 hereof; and

(c) This Warrant.

Upon the exercise of the rights represented by this Warrant, a certificate or certificates for the Exercise Shares so purchased, in the name of the Holder or persons affiliated with the Holder, if the Holder so designates, shall be issued and delivered to the Holder within a reasonable time after the rights represented by this Warrant shall have been so exercised, and, if this Warrant has not been fully exercised or converted and has not expired, a new Warrant representing the Shares not so acquired shall be issued and delivered to the Holder within a reasonable time after the rights represented by this Warrant shall have been so exercised.

The person in whose name any certificate or certificates for the Exercise Shares are to be issued upon exercise of this Warrant shall be deemed to have become the holder of record of such shares on the date on which this Warrant was surrendered and payment of the Exercise Price was made, irrespective of the date of delivery of such certificate or certificates, except that, if the date of such surrender and payment is a date when the stock transfer books of the Company are closed, such person shall be deemed to have become the holder of such shares at the close of business on the next succeeding date on which the stock transfer books are open.

2.2 Net Exercise. Notwithstanding any provisions herein to the contrary, if the fair market value of one share of the Common Stock is greater than the Exercise Price (at the date of calculation as set forth below), in lieu of exercising this Warrant by payment of cash, the Holder may elect to receive shares equal to the value (as determined below) of this Warrant (or the portion thereof being canceled) by surrender of this Warrant at the principal office of the Company together with the properly completed and endorsed Notice of Exercise, in which event the Company shall issue to the Holder a number of shares of Common Stock computed using the following formula:

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For purposes of the above calculation, the fair market value of one share of Common Stock shall mean the average of the closing bid and asked prices of Common Stock quoted in the over-the-counter market in which the Common Stock is traded or the closing price quoted on any exchange on which the Common Stock is listed, whichever is applicable, as published in the Eastern Edition of The Wall Street Journal for the ten (10) trading days prior to the date on which this Warrant is surrendered and payment of the Exercise Price has been paid (or such shorter period of time during which such stock was traded over-the-counter or on such exchange). If the Common Stock is not traded on the over-the-counter market or on an exchange, the fair market value shall be the price per share that the Company could obtain from a willing buyer for Common Stock sold by the Company from authorized but unissued shares, as such price shall be determined in good faith by the Company’s Board of Directors.

3. COVENANTS OF THE COMPANY. The Company covenants and agrees that all the Exercise Shares that may be issued upon the exercise of the rights represented by this Warrant will, upon issuance, be validly issued and outstanding, fully paid and nonassessable. The Company further covenants and agrees that the Company will at all times during the Exercise Period have authorized and reserved a sufficient number of shares of its Common Stock to provide for the exercise of the rights represented by this Warrant.

4. REPRESENTATIONS OF HOLDER.

4.1 Acquisition of Warrant for Personal Account. The Holder represents and warrants that it is acquiring the Warrant and the Exercise Shares solely for its account for investment and not with a view to or for sale or distribution of said Warrant or the Exercise Shares or any part thereof. The Holder also represents that the entire legal and beneficial interests of the Warrant and the Exercise Shares the Holder is acquiring is being acquired for, and will be held for, its account only.

4.2 Securities Are Not Registered.

(a) The Holder understands that the Warrant and the Exercise Shares have not been registered under the Securities Act of 1933, as amended (the “Act”) on the basis that no distribution or public offering of the stock of the Company is to be effected. The Holder realizes that the basis for the exemption may not be present if, notwithstanding its representations, the Holder has a present intention of acquiring the securities for a fixed or determinable period in the future, selling (in connection with a distribution or otherwise), granting any participation in, or otherwise distributing the securities. The Holder has no such present intention.

(b) The Holder recognizes that the Warrant and the Exercise Shares must be held indefinitely unless they are subsequently registered under the Act or an exemption from such registration is available. The Holder recognizes that the Company has no obligation to register the Warrant or the Exercise Shares of the Company, or to comply with any exemption from such registration.

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(c) The Holder is aware that neither the Warrant nor the Exercise Shares may be sold pursuant to Rule 144 adopted under the Act unless certain conditions are met, including, among other things, the existence of a public market for the shares, the availability of certain current public information about the Company, the resale following the required holding period under Rule 144 and the number of shares being sold during any three month period not exceeding specified limitations.

4.3 Disposition of Warrant and Exercise Shares.

(a) The Holder further agrees not to make any disposition of all or any part of the Warrant or the Exercise Shares in any event unless and until:

(i) There is then in effect a registration statement under the Act covering such proposed disposition and such disposition is made in accordance with said registration statement;

(ii) The Holder shall have notified the Company of the proposed disposition and shall have furnished the Company with a detailed statement of the circumstances surrounding the proposed disposition, and if reasonably requested by the Company, the Holder shall have furnished the Company with an opinion of counsel, reasonably satisfactory to the Company, for the Holder to the effect that such disposition will not require registration of such Warrant or the Exercise Shares under the Act or any applicable state securities laws; or

(iii) The Company shall have received a letter secured by the Holder from the Securities and Exchange Commission stating that no action will be recommended to the Commission with respect to the proposed disposition.

(b) The Holder understands and agrees that all certificates evidencing the shares to be issued to the Holder may bear the following legend:

THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR UNDER THE SECURITIES LAWS OF CERTAIN STATES. THESE SECURITIES MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED EXCEPT AS PERMITTED UNDER THE AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT, THE ACT AND APPLICABLE STATE SECURITIES LAWS PURSUANT TO REGISTRATION OR AN EXEMPTION THEREFROM. THE ISSUER OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL SATISFACTORY TO THE ISSUER THAT SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION OTHERWISE COMPLIES WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS. THESE SECURITIES MAY BE PLEDGED IN CONNECTION WITH A

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BONA FIDE MARGIN ACCOUNT WITH A REGISTERED BROKER-DEALER OR OTHER LOAN WITH A FINANCIAL INSTITUTION THAT IS AN “ACCREDITED INVESTOR” AS DEFINED IN RULE 501(a) UNDER THE SECURITIES ACT OR OTHER LOAN SECURED BY SUCH SECURITIES.

5. ADJUSTMENT OF EXERCISE SHARES AND EXERCISE PRICE.

(a) Stock Splits, Combinations, etc. In the event of changes in the outstanding Common Stock of the Company by reason of stock dividends, split-ups, recapitalizations, reclassifications, combinations or exchanges of shares, separations, reorganizations, liquidations, or the like, the number and class of shares available under the Warrant in the aggregate and the Exercise Price shall be correspondingly adjusted to give the Holder of the Warrant, on exercise for the same aggregate Exercise Price, the total number, class, and kind of shares as the Holder would have owned had the Warrant been exercised prior to the event and had the Holder continued to hold such shares until after the event requiring adjustment. The form of this Warrant need not be changed because of any adjustment in the number of the Exercise Shares subject to this Warrant. The foregoing provisions of this Section 5(a) shall similarly apply to successive stock dividends, split-ups, recapitalizations, reclassifications, combinations or exchanges of shares, separations, reorganizations, liquidations, or the like and to the stock or securities of any other entity that are at the time receivable upon the exercise of this Warrant.

(b) Merger, Sale of Assets, etc. If at any time while this Warrant, or any portion hereof, is outstanding and unexpired there shall occur (i) the sale, conveyance, exchange, license or other transfer of all or substantially all of the intellectual property or assets of the Company, (ii) any acquisition of the Company by means of a consolidation, stock exchange, merger or other form of corporate reorganization of the Company with any other corporation in which the Company’s stockholders prior to the consolidation or merger own less than a majority of the voting securities of the surviving entity or (iii) any transaction or series of related transactions following which the Company’s stockholders prior to such transaction or series of related transactions own less than a majority of the voting securities of the Company (collectively, a “Change of Control”), this Warrant shall cease to represent the right to receive the Exercise Shares and shall automatically and without further action represent the right to receive upon exercise of this Warrant, during the period specified herein and upon payment of the Exercise Price then in effect, the number of shares of stock or other securities or property offered to the Company’s holders of Common Stock in connection with such Change of Control that a holder of the shares deliverable upon exercise of this Warrant would have been entitled to receive in such Change of Control if this Warrant had been exercised immediately before such Change of Control, subject to further adjustment as provided in this Section 5. The foregoing provisions of this Section 5(b) shall similarly apply to successive reorganizations, consolidations, mergers, sales and transfers and to the stock or securities of any other entity that are at the time receivable upon the exercise of this Warrant. If the per share consideration payable to the holder hereof in connection with any such transaction is in a form other than cash or marketable securities, then the value of such consideration shall be determined in good faith by the Company’s Board of Directors. In all events, appropriate adjustment (as determined in good faith by the Company’s Board of Directors) shall be made in the application of the provisions of

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this Warrant with respect to the rights and interests of the Holder after the transaction, to the end that the provisions of this Warrant shall be applicable after that event, as near as reasonably may be, in relation to any shares or other property deliverable after that event upon exercise of this Warrant.

6. FRACTIONAL SHARES. No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All Exercise Shares (including fractions) issuable upon exercise of this Warrant may be aggregated for purposes of determining whether the exercise would result in the issuance of any fractional share. If, after aggregation, the exercise would result in the issuance of a fractional share, the Company shall, in lieu of issuance of any fractional share, pay the Holder otherwise entitled to such fraction a sum in cash equal to the product resulting from multiplying the then current fair market value of an Exercise Share by such fraction.

7. NOTICE OF CERTAIN EVENTS. The Company shall provide to the Holder at least five (5) days advance written notice of any event that would result in an adjustment to the Exercise Shares or Exercise Price pursuant to Section 5 hereof.

8. MARKET STAND-OFF AGREEMENT. In connection with any public offering of securities of the Company registered under the Act, the Holder hereby agrees not to sell, transfer, make any short sale of, grant any option for the purchase of, enter into any hedging or similar transaction with the same economic effect as a sale or otherwise transfer or dispose of any Common Stock (or any other securities of the Company) held by the Holder (other than those included in the registration) for a period of one hundred eighty (180) calendar days following the effective date of a registration statement of the Company filed under the Act in connection with such offering (or such other period as may be requested by the Company or an underwriter to accommodate regulatory restrictions on (i) the publication or other distribution of research reports and (ii) analyst recommendations and opinions, including, but not limited to, the restrictions contained in NASD Rule 2711(f)(4) or NYSE Rule 472(f)(4), or any successor provisions or amendments thereto). The Holder agrees to execute and deliver such other agreements as may be reasonably requested by the Company or the underwriter that are consistent with the Holder’s obligations under this Section 8 or that are necessary to give further effect thereto. The Company may impose stop-transfer instructions with respect to the shares of Common Stock (or any other securities) subject to the foregoing restriction until the end of the market stand-off day period.

9. NO STOCKHOLDER RIGHTS. This Warrant in and of itself shall not entitle the Holder to any voting rights or other rights as a stockholder of the Company.

10. TRANSFER OF WARRANT. Subject to applicable laws and the restriction on transfer set forth on the first page of this Warrant, this Warrant and all rights hereunder are transferable, by the Holder in person or by duly authorized attorney, upon delivery of this Warrant and the form of assignment attached hereto to any transferee designated by the Holder. The transferee shall sign an investment letter in form and substance satisfactory to the Company.

11. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT. If this Warrant is lost, stolen, mutilated or destroyed, the Company may, on such terms as to indemnity

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or otherwise as it may reasonably impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed. Any such new Warrant shall constitute an original contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated or destroyed Warrant shall be at any time enforceable by anyone.

12. NOTICES, ETC. Any notices required or permitted hereunder shall be in writing and shall be deemed effectively given: (a) upon personal delivery to the party to be notified, (b) when sent by confirmed telex or facsimile if sent during normal business hours of the recipient, if not, then on the next business day, (c) five (5) days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (d) one (1) day after deposit with a nationally recognized overnight courier, specifying next day delivery, with written verification of receipt. All communications shall be sent to the Company or to the Holder at their respective addresses set forth above or at such other address as the Company or the Holder may designate by ten (10) days advance written notice to the other parties hereto.

13. ACCEPTANCE. Receipt of this Warrant by the Holder shall constitute acceptance of and agreement to all of the terms and conditions contained herein.

14. GOVERNING LAW. This Warrant and all rights, obligations and liabilities hereunder shall be governed by the laws of the State of Delaware.

*  *  *  *  *  *

IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by its duly authorized officer as of January 13, 2010.

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NOTICE OF EXERCISE

TO:  LUNA INNOVATIONS INCORPORATED

(1) The undersigned hereby irrevocably elects to purchase             shares of the Common Stock of LUNA INNOVATIONS INCORPORATED (the “Company”) pursuant to the terms of the attached Warrant, and tenders herewith payment of the exercise price in full, together with all applicable transfer taxes, if any.

The undersigned hereby irrevocably elects to purchase             shares of the Common Stock of LUNA INNOVATIONS INCORPORATED (the “Company”) pursuant to the terms of the net exercise provisions set forth in Section 2.2 of the attached Warrant, and shall tender payment of all applicable transfer taxes, if any. Net-issue information, calculated in accordance with Section 2.2 of the attached Warrant, is as follows:

(2) Please issue a certificate or certificates representing said shares of Common Stock in the name of the undersigned or in such other name as is specified below:

(3) The undersigned represents that (i) the aforesaid shares of Common Stock are being acquired for the account of the undersigned for investment and not with a view to, or for resale in connection with, the distribution thereof and that the undersigned has no present intention of distributing or reselling such shares; (ii) the undersigned is aware of the Company’s business affairs and financial condition and has acquired sufficient information about the Company to reach an informed and knowledgeable decision regarding its investment in the Company; (iii) the undersigned is experienced in making investments of this type and has such knowledge and background in financial and business matters that the undersigned is capable of evaluating the merits and risks of this investment and protecting the undersigned’s own interests; (iv) the undersigned understands that the shares of Common Stock issuable upon exercise of this Warrant have not been registered under the Securities Act of 1933, as amended (the “Securities

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Act”), by reason of a specific exemption from the registration provisions of the Securities Act, which exemption depends upon, among other things, the bona fide nature of the investment intent as expressed herein, and, because such securities have not been registered under the Securities Act, they must be held indefinitely unless subsequently registered under the Securities Act or an exemption from such registration is available; (v) the undersigned is aware that the aforesaid shares of Common Stock may not be sold pursuant to Rule 144 adopted under the Securities Act unless certain conditions are met and until the undersigned has held the shares for the time period prescribed by Rule 144; and (vi) the undersigned agrees not to make any disposition of all or any part of the aforesaid shares of Common Stock unless and until there is then in effect a registration statement under the Securities Act covering such proposed disposition and such disposition is made in accordance with said registration statement, or the undersigned has provided the Company with an opinion of counsel satisfactory to the Company, stating that such registration is not required.

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ASSIGNMENT FORM

(To assign the foregoing Warrant, execute this form and supply required information. Do not use this form to purchase shares.)

FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced thereby are hereby assigned to

Dated:                     , 20    

NOTE: The signature to this Assignment Form must correspond with the name as it appears on the face of the Warrant, without alteration or any change whatever. Officers of corporations and those acting in a fiduciary or other representative capacity must present proper evidence of authority to assign the foregoing Warrant.

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